I personally believe that we are all here to learn a specific lesson or to discover something about a deeper part of ourselves. Whatever the reason we are here, some of us just can’t shake it: we need to know more about ourselves spiritually. Gemstones are a great way to do this, but so is astrology. Mixing the two can bring accelerated results to uncovering mystical secrets locked away in our subconscious. As I have researched and used various gemstones, I have noticed that some sun signs work better with certain gemstones than others.
So what gemstones work best with each zodiac sign? Here is a list of best gemstones for each zodiac sign to help with spiritual growth:
- Aries: Bloodstone
- Taurus: Lapis Lazuli
- Gemini: Chrysocolla
- Cancer: Black Tourmaline
- Leo: Malachite
- Virgo: Lepidolite
- Libra: Citrine
- Scorpio: Smoky Quartz
- Sagittarius: Turquoise
- Capricorn: Moonstone
- Aquarius: Aragonite
- Pisces: Rose Quartz
This article goes over each zodiac sign, the spiritual lesson they are here to learn, and the best gemstones for their spiritual progression.
Zodiac Gemstones Reference Guide
Below is a reference guide to see which sign correlates to each birth date, so you can find which sign you are. Also included are the planets that the sign is ruled by, which provides insight into the energy patterns of each sun sign. This chart also includes a list of gemstones that work best with that sign for spiritual growth.
|Zodiac Sign||Birth Dates||Planet||Gemstones|
|Aries||March 21 – April 19||Mars|
|Bloodstone, Tiger’s Eye, Tangerine Quartz, Red Tourmaline, Golden Topaz|
|Taurus||April 20 – May 20||Venus|
|Lapis Lazuli, Celestite, Blue Opal, Iolite, and Kyanite|
|Gemini||May 21 – June 20||Mercury|
|Chrysocolla, Malachite, Green Jade, Red Beryl, Green Kyanite|
|Cancer||June 21 – July 22||Moon|
|Black Tourmaline, Smoky Quartz, Shungite, Moonstone, Kambaba Jasper|
|Leo||July 23 – August 22||Sun|
|Malachite, Red Jade, Fushite, Ametrine, Amber|
|Virgo||August 23 – September 22||Mercury/Ceres|
|Lepidolite, Lapis Lazuli, Iceland Spar, Rainbow Fluorite, Pink Danburite|
|Libra||September 23 – October 22||Venus|
|Citrine, Carnelian, Pyrite, Amber, Red Jade|
|Scorpio||October 23 – November 21||Mars/Pluto|
|Smoky Quartz, Black Obsidian, Shungite, Black Tourmaline, Hematite|
|Sagittarius||November 22 – December 21||Jupiter|
|Turquoise, Lapis Lazuli, Blue Kyanite, Blue Flourite, Celestite|
|Capricorn||December 22 – January 19||Saturn |
|Moonstone, Selenite, Amethyst, Clear Quartz, and Apophyllite|
|Aquarius||January 20 – February 18||Saturn/Uranus|
|Aragonite, Desert Rose, Calcite, Rhodonite, and Garnet|
|Pisces||February 19 – March 20||Jupiter/Neptune|
|Rose Quartz,Selenite, Pink Danburite, Pink Halite, and Fuchsite|
Characteristics of Each Zodiac Sign & Their Spiritual Lessons
March 21 – April 19
Spiritual Lesson: Release control and surrender to the flow of the universe.
Aries is ruled by the planet Mars and the element of fire, so it is no wonder that they exert their strong willpower in order to get things done. They love working hard to see results.
Those who have an Aries sun sign are manifesters and creators. They like to be active, and can’t stand being still for any amount of time. They like to be the leaders of projects, so they can control the pace at which things go, and they like things to go fast.
However, their need for control and stubbornness can make them miss out on the synchronistic power of the universe. Their “create then move on” mentality does not let them enjoy the opportunities that the universe gives them to make their creation even greater.
Because of this, they can feel burnt out on projects that they start, and give the power over to others while they move on and start something else. If they trust that the universe will meet them half-way, things will manifest without them having to exert so much energy. This gives them the potential to be a non-stop manifester/generator.
The keywords for Aries are trust and surrender. Aries can adopt an attitude that if they don’t pull the trigger, nothing will ever get done. Their spiritual lesson is to slow down, take a step back, and pay attention to the magic that is unfolding in the present moment. The universe can help guide them on the next steps without them having to bulldoze a path from scratch.
Gemstones that can help Aries with spiritual progression include anything that will get them out of the future and into the present moment, and help them align to the universal energies that are flowing around them.
This stone is a blend of high vibrational chalcedony, with heavy metals of the earth that give it a stone that acts as a yin-yang balance.
Bloodstone balances the subtle energies of the body and brings one into the present moment. It enhances one’s strength by incorporating the lightness of air to the heavy physical energies; it is a balance of inner strength and outer strength.
It brings in higher energies so that the fast-moving Aries can see the subtle energies of the universe and allow them into their reality.
Ritual: For Aries, slowing down is what is necessary for this spiritual lesson. A great ritual for Aries to do this is to practice self-care at home. Taking a bath infused with bloodstone can be extremely effective at balancing the entire system.
Run a warm bath and place 1-5 polished pieces of bloodstone at the bottom of the tub, near where the feet sit. Fill the bath with grounding essential oils: cedarwood, sandalwood, frankincense, patchouli, etc. Rest in the bath for 15-30 minutes, and let yourself relax. Try breathing techniques to get in the present moment.
This ritual brings in all four elements: fire, earth, air, and water.
Other gemstones that help Aries with spiritual growth include: Tiger eye, tangerine quartz, red tourmaline, and golden topaz
April 20 – May 20
Spiritual Lesson: Release the urge to fix everyone’s problems.
Taurus is a problem solver. They like to be the superheroes of their friend’s lives, always rushing to the aid of a friend in need. They often take on more responsibility than they need to, because they automatically feel that it is their responsibility to fix something, even if nobody asked them to.
However, not everyone should have their problems fixed for them. Without facing our own challenges, we will never learn and grow. This is the lesson for Taurus: let people learn their own lessons.
It is important for Taurus to understand the deeper implications of solving other people’s problems. Those people will still have to learn their own lessons eventually, and the longer they have to learn them, the harder they will be as time goes on.
The lesson for Taurus to learn is to say “no,” or instead of fixing it, be patient and show them how to do it so that they know for next time.
This is an activating stone that enhances intuition. It works on the third eye and throat center, which is is where telepathic communication, intuitive knowledge, and karmic agreements rest.
Taurus tends to have a lot of karma with other people in this lifetime, which is why they have a need to solve everyone’s problems.
Lapis Lazuli helps bring those karmic agreements into the present moment and allows Taurus to finally move past them. With every karmic contract that gets finished, they feel less and less guilt saying “no.”
Ritual: Keep a polished Lapis Lazuli stone in your pocket or purse. Every time you feel the need to solve someone’s problem, take it out and hold it in your left hand. This hand represents what you are releasing.
Take a moment and intuitively ask if it is a good idea for you to solve that person’s problem, or if you should guide them some other way. The energy of Lapis Lazuli will help you get clarity on the issue.
Other gemstones that help Taurus with spiritual growth: Celestite, blue opal, iolite, and kyanite.
May 21 – June 20
Spiritual Lesson: Love and accept all parts of yourself.
Because of their intelligent and witty nature, Geminis can be very critical of the outside world, and they do not see this as a character flaw. It is how they understand what is making people successful and what is holding them back. They can feel frustrated with people who don’t have enough clarity on a situation to make the right decision.
However, this also means that they are overly critical of themselves. Everything that is projected onto others is also projected onto oneself; this is the law of nature.
Geminis can get stuck in a cycle of self-criticizing thoughts until they are so unhappy with their circumstances that they have to make drastic life changes, such as break up with a partner, move to a different city, change a job or disappear from everyone and everything.
The spiritual lesson for Geminis is to learn how to love and accept themselves, by learning how to love and accept the people and situations in their environment. It is important for them to be comfortable feeling agitation towards someone, and not act on it. Let the feeling arise, sit with it, and let it pass away.
The best gemstones for Gemini are related to self-acceptance and being grounded in their environment. They should focus on strengthening their heart center, as Geminis tend to have weak parts of the body around the heart such as lungs, shoulders, and arms.
This stone strengthens the heart center, grounds one to the earth, and helps tune one’s energy to their own inner wisdom. It encourages one to love and accept all the phases of life, including the negative aspects. It lets one know that changing the circumstances will not heal the heart; only staying still and accepting oneself fully will lead to deep spiritual growth.
Ritual: Chrysocolla assists in bringing you to the present moment by aligning yourself with the energies of the earth, while staying connected to your ruling planet, Mercury.
Take a piece of chrysocolla and go outside. Take your shoes and socks off and feel the earth on your bare feet. Hold your piece of chrysocolla on your heart center. Imagine there are little magnets on the bottoms of your feet which is pulling the earth energy up through your feet. Have it flow up your chakra channels and release out of the top of your head. Have it split at your shoulders and go down your arms and out your hands, into the piece of chrysocolla above your heart.
Say the affirmation: “I belong here. I love and accept myself fully. I love and accept my reality fully”
If difficult emotions come up, such as negativity, frustration, sadness or agitation, this is a great opportunity to let yourself feel those emotions without running away from them.
Other gemstones that help Geminis with spiritual growth: Malachite, Green Jade, Red Beryl (Bixbite), Green Kyanite
June 21 – July 22
Spiritual Lesson: Learn to set energetic and emotional boundaries.
Ruled by the moon and the element of water, Cancers are highly influenced by their emotions, making them the most sensitive of all the zodiac signs.
They are highly intuitive and are keenly aware of any emotional tensions that someone is feeling. It is unsettling for them to feel other people’s sadness, anxiety or depression, so they will do whatever it takes to stabilize any turbulent emotions. Even if it means giving up their own emotional energy to do it.
Cancers are the healers and empaths. But often that results in them feeling like they have to emotionally protect themselves, and hide behind the hard shell of their crab exterior. They can feel emotionally drained, making it hard for them to stick to their commitments.
The lesson for Cancer is to learn where their energy ends and other people’s energy begins so that they can set healthy energetic boundaries. They must learn how to not give so much energy away to others, so they can have a high enough energy level to say “YES!” to any event.
Black Tourmaline is the stone of protection. It helps protect the edge of the aura from negative energy “whacking” through, causing damage to the energetic field. It also helps the person carrying it to understand their own energy, and where their aura begins and ends.
Cancers should carry a small piece of tourmaline in their pocket or purse, and can even sleep with it if they have issues with nightmares. It will help them get rid of other people’s energy that they are holding onto.
Ritual: Because Cancer is ruled by the element of water, this medium is great for auric protection and psychic cleansing.
Put a piece of tourmaline in a small spray bottle and fill with filtered water. Add high vibrational essential oils of rose or another essential oil of your choice. Let sit on a window sill overnight under a full moon.
In the morning, it is ready and activated. Spray the tourmaline-infused water in a rainbow shape above your head for a quick cleansing of your aura. Do this each morning and evening until the next full moon.
Other gemstones that can help Cancers with spiritual growth: Smoky Quartz, Shungite, Moonstone, Kambaba Jasper
July 23 – August 22
Spiritual Lesson: Not everyone has to love you for you love yourself.
Ruled by the Sun and the element of fire, it is hard to not notice a Leo in the room because they shine so bright. They love to be the center of attention, and there are no shortages of people wanting to be their friend or romantic partner.
Leos get their self-worth and value by how brightly they can shine, and how many people they can influence. They don’t like being alone, because they feel that their true value only amounts to what other people can see, hear and touch.
They can tend to hold onto unhealthy relationships, friendships and partnerships for too long, because they don’t want to let go of the value that the relationship once gave them. This can turn into an unhealthy or manipulative game of ping pong, leaving both parties feeling exhausted in the end.
The spiritual lesson for Leos is to let people go that they are holding onto for vanity reasons, especially ex-lovers. This can leave room for introspection, and learning how to love oneself without the affirmation of friends and lovers.
Malachite holds onto an unusual blend of solar plexus and heart energy, both of which are necessary for Leo’s spiritual development. Leos tend to have an overactive solar plexus chakra that pulls from the heart chakra center.
Using this stone can bring back some of that firey confidence into the heart center, so Leos can open a gateway to self-love and acceptance.
While this stone is a deep shade of green, it gets its color from the high amounts of copper, which is usually a rose gold to brown color. Don’t let the green fool you, this is a very active stone.
Ritual: The best practice that Leos can start doing every day is meditation. This is an activity that is done alone and can help Leos train to focus their bursts of energy and active mind.
Hold a piece of malachite in your right hand. As you meditate, feel the energy from your solar plexus chakra opening up your heart chakra. Metta meditation is great for this ritual.
You can even lay down while you meditate and place a piece of malachite directly on your heart center or solar plexus chakra center.
Other gemstones that can help Leos with spiritual growth: Red Jade, Fushite, Ametrine, Amber
August 23 – September 22
Spiritual Lesson: Appreciate failure as a part of growth.
Virgos are ruled by the planet Mercury and the element of earth, so they are intelligent and grounded people. They love logic and practicality and like to keep working at a problem until they find a solution.
They can get fixated on finding solutions to problems, so they can tend to create complexities that weren’t there before, just to have something to solve! This gives them an anxious disposition because they are always expecting problems to arise.
Their earth element gives them the urge to seek perfection, making them very hard on themselves. If they are not successful at something, they can stew on their failure until they feel worthless or depressed.
Their spiritual lesson is to not get too be too hard on oneself if a task isn’t completed to perfection, and to embrace imperfection and failure as the law of nature. Failure is how we grow. Instead, appreciate the life lesson, and let go of defeat.
The stone Lepidolite is very calming to the nervous system, and assists at calming anxious thoughts. It contains lithium, which is a chemical that is used in pharmaceutical psychiatric meditations because of its calming ability.
Having this stone nearby will ground the nervous energy that Virgos feel so that they can embrace their uncomfortableness as part of a larger learning experience. It can transmute that anxiety into playful carefree energy, which Virgos can use from time to time.
Ritual: Keep a “no to-do” list, where you write down how you feel instead of writing about all your goals and things you need to get done. Hold a piece of lepidolite as you write, as it can be calming and give you clarity on the root of your anxiety.
Once you can put your feelings on paper, it may be easier to manage them more throughout your day.
Other gemstones that help Virgo with spiritual growth: Lapis lazuli, Iceland spar, Rainbow Fluorite, and Pink danburite.
September 23 – October 22
Spiritual Lesson: Start living your own life instead of helping others live theirs.
Libras are kind to their core, as they are ruled by the loving Venus and the carefree element of air. They get their meaning in life by flittering around from one situation to the next, helping out wherever they can.
They love to see others succeed and being a part of the story that got them there. On top of being helpful and kind, they are also charming, genuine, social and fun to be around.
Their biggest downfall is the inability to feel confident in their own decisions to make their own life successful. They are so busy helping others that they often forget to help themself. This leaves them on the sidelines cheering while other people win the race. Often, their friends move on without them, as they out-grow their flittery Libra friend.
The life lesson for Libra is to learn to be confident and begin to believe that you are capable and worthy of being successful.
The best gemstone that Libras can work with is Citrine, as it strengthens the solar plexus chakra that is all about self-expression, confidence and manifesting a higher reality. Citrine is the abundance stone and will help clear out blocked energy that is preventing Libras from keeping success at an arm’s length.
Citrine has a high vibration that resonates well with the flittery energy of a Libra, so Libras do not feel burnt out when they work with citrine for long periods of time.
Ritual: Citrine is a beautiful stone and a great piece to have as a decoration in the house or office. Using citrine in the energy practice of Feng Shui can move a lot of energy.
The abundance and money area is in the Southeast corner of your home or office. If possible, place a large piece or a few smaller pieces in the southeast corner of your home. But, citrine in any area of your home will move more abundance energy, so place citrine where it looks nice and gets a lot of attention: on a bookshelf, on the back of the toilet, on a fireplace mantel, etc.
Other gemstones that help Libras with spiritual growth: Carnelian, Pyrite, Amber, Red Jade.
October 23 – November 21
Spiritual Lesson: Don’t let your grudges get the best of you.
Scorpios are deep feelers, being ruled by the element of water and the planet Pluto. But they are also ruled by the planet Mars, which is all about aggressive control over a situation. So if Scorpios are slighted in any way, they want to act on their hurt emotions. This leads them to want to seek revenge, and they rarely forget once they hold a grudge against someone.
Holding a lot of anger or resentment in the body can lead to physical illness, as unprocessed emotions can cause issues with digestion, spleen, gall bladder, liver, and throat/thyroid. They don’t know how to process their emotions without taking action in some way, represented by the sting of a scorpion.
The lesson for Scorpio is finding other outlets for processing emotions other than seeking revenge. Instead of acting out a scene from a mid-day soap opera, their efforts would be better spent finding energetic tools to help them release that anger.
Smoky quartz is a jack-of-all-trades gemstone, but it works particularly well with helping the psyche process un-digested energy or emotions. Scorpios do well with any quartz crystals and the dark addition to the classic clear quartz lets the deeper, darker emotions come to the surface.
Ritual: Scorpios do well with any kind of shadow work and incorporating the smoky quartz crystal will accelerate the emotions processed in shadow work activities.
Here is information on shadow work if Scorpios are interested: What is shadow work? (And how to do it.)
Other gemstones that help Scorpios with spiritual growth: Black Obsidian, Shungite, Black Tourmaline, and Hematite.
November 22 – December 21
Spiritual Lesson: Learn how to turn your passion into your work so you can play every day.
Saggitarius is ruled by the element fire, giving them an inner fire of passion, adventure, and adrenaline rushes. They like to have fun, and have a carefree attitude towards life. They are also ruled by the mysterious and slow-moving planet Jupiter, which is an energy that conflicts with the passionate fire burning within them.
Often this results in a Saggitarus that has loads of energy to have fun, but if there isn’t passion in something, there will likely be no energy given to it. Things like cleaning, work, taxes, and general life adulting are not activities that Saggitariuses are very fond of.
Saggitarius is often mislabeled as “lazy” when that really isn’t the case. They are selectively energized people – they can outperform most people at things they love, but couldn’t care less to compete at anything they are dispassionate about.
The spiritual lesson for Saggitarius is to cultivate a lifestyle that utilizes that passion for the betterment of themselves or the world at large. It would be helpful for Saggitarius to understand what gets them energized, and try to make a living at doing that. It is also helpful for Saggitarius to learn to delegate tasks that are boring, so they can utilize their energy elsewhere.
Saggitarius lives most of their life in their lower three chakras, especially in their solar plexus chakra. This is where the element of fire gives them their life force energy. But the energy of Jupiter resonates well with the throat and third eye chakra. Bringing in the energy of Jupiter will help bring in more clarity and foresight into potential business ideas.
Turquoise can be a helpful stone to help Saggitarius align with these energies and feel comfortable with more energy in their throat and third eye. This lighter energy may help Saggitarius feel more motivated, and give them the endurance to stick with long-term projects.
Ritual: Turquoise is a beautiful stone that can be worn as a necklace, set of earrings or a ring. It may be helpful for Saggitarius to incorporate turquoise jewelry into their wardrobe so they can have consistent high vibrational energy in their energy field without having to do much extra work.
Men can put a piece of turquoise in their pocket, or wear turquoise on a belt buckle.
Other stones that help Saggitarius with spiritual growth: Lapis Lazuli, Blue Kyanite, Blue Flourite, and Celestite.
December 22 – January 19
Spiritual Lesson: It’s ok to live life on the edge sometimes.
Capricorns are ruled by the earth, which gives them the need for security, and the planet Saturn, which gives them the need for forwarding movement. This makes Capricorns amazing at business. Always burning the candle at both ends, they feel as though no amount of work can be enough if it means giving them more financial security.
The constant need to feel secure can make Capricorns have a very narrow comfort zone. They can come across as introverted, cautious and calculated because they don’t like being in situations where they haven’t planned every possible outcome.
This mentality closes Capricorns off to the spontaneous magic that can happen without a plan. It can lead Capricorns into a lifestyle of strict routine, with limited time for adventures.
The spiritual lesson for Capricorns can be summed up with the quote by Neale Donald Walsch: “Life begins at the end of your comfort zone.” Capricorns love learning new things and having new experiences, but they often limit the opportunities for this to occur. Get outside, go travel, and take more vacations.
Getting out of the root chakra and into the upper chakras is a great practice or Capricorns to bring into their daily routine. Moonstone is an amazing crystal for clearing any blockages up to the upper chakras, in a gentle way. It helps transmute the anxious energy into love and kindness towards oneself and the world. It opens gateways into appreciating the magic that is always unfolding in one’s life.
Ritual: Capricorns would do well with connecting to their crown chakra, which opens them up to the synchronicities of the universe.
They are actually very intuitive but often can turn this voice off. Moonstone can retune this energy so that their intuition is awakened once again.
Meditation can help Capricorns break away from the need to constantly be moving. Sometimes doing nothing can produce the best results.
Each morning, take a piece of Moonstone and hold it in your hands while you meditate. Try not to think of anything for those three minutes. If you catch yourself worrying or creating a to-do list, gently return to the meditation with kindness and acceptance.
Other gemstones that help Capricorns with spiritual growth: Selenite, Amethyst, Clear Quartz, and Apophyllite.
January 20 – February 18
Spiritual Lesson: Step back from your imagined reality and be grateful for what you have right now.
Aquarius is ruled by the element of air, which means that they live their life through the lens of their imagination. They are always imagining new and innovative ways to make their reality better. This, coupled with their ruling planets forward-moving Saturn and mystical Neptune, give Aquarius an especially vivid imagination that they want to see manifested in their reality.
While Aquarius has no problem being an active participant in the world, they also live half their life in their own head. This sets them up to always see a better version of what is in front of them. In the rush to keep moving to make things better, they can often miss out on appreciating what is in front of them.
The spiritual lesson for Aquarius is to be patient, slow down, and periodically step back into the present moment. While growth is not bad, everything that grows has periods of rest and hibernation.
Aragonite is a stone of balance, particularly with its ability to bring in the natural balance of the earth. It resonates with the energy of the earth, which can ground the flittery airiness of Aquarius. It helps slow down the mind and brings the energy back to center.
It is best used out in nature and in a quiet place. Using aragonite can help Aquarius feel calm and will help them open their energy to the magic happening in their current reality.
Ritual: The best activities for Aquarius to do are meditative, without actually meditating. They should turn their introspective mind off and work on something physical.
A great hobby for Aquariuses to try is gardening. This connects them with the earth and gets them out of their heads and into the soil. Placing pieces of aragonite near the plants and in the garden bed brings in wonderful plant energy.
Other gemstones that help Aquarius with spiritual growth: Desert Rose, Calcite, Rhodonite, and Garnet.
February 19 – March 20
Spiritual Lesson: Trust your intuition and take action when you feel the intuitive message is “let go.”
Pisces are loyal lovers and if they feel emotionally attached to someone, they will put that person’s needs above all else. They are ruled by the element of water, making them sensitive and attentive to the emotions of others. Mixed with slow-moving Jupiter, they will fight to keep the ones they love in their life and are ready to settle down the moment they get in a partnership. With a sprinkle of mystical Neptune, they are intuitive and live life from moment to moment of their feelings.
The nature of feelings is very up and down, just like the mindset of Pisces. They can be overjoyed one moment, then depressed the next moment. They can feel confident one moment, then insecure the next moment.
The voice of intuition is very loud in the ears of Pisces, and they learn that they should always trust their gut. However, letting go of the past and moving on to more emotionally healthy situations is difficult for them. They have a tendency to fall into long-term partnerships that are not healthy, even when their intuition tells them to leave. It is hard to let anyone they love go.
For Pisces to take spiritual steps, they should practice letting people go from their life who are causing them to be emotionally unstable. This is a life-long practice and should be done by joining healthy groups in the community that can give support and encouragement.
Rose Quartz has a high vibration that resonates well with Pisces energy. This gemstone resonates with energy in the heart center and will bring any imbalances in the heart back to the center.
It is great for those needing to move past old lovers or to give oneself more love. It is a stone of acceptance of the present moment and forgiveness.
Ritual: Because Pisces are lovers, practicing Metta meditation would be a great practice for them to incorporate into their daily routine.
Metta meditation is also called loving-kindness meditation, and through the process of meditation, you feel and imagine giving love to yourself, giving love to others, and giving love to the world.
While doing Metta meditation each morning or evening, hold a rose quartz crystal to your heart. This will help transmute any negative or unbalanced emotions into universal consciousness, sending it back to the original source.
Other gemstones that help Pisces with spiritual growth: Selenite, Pink Danburite, Pink Halite, and Fuchsite.
Take a moment and think of the spiritual lessons you are trying to learn in this lifetime. Are they related to your zodiac? Are there other crystals that you think might help you along your spiritual journey?
These are all helpful questions to ask oneself, and no matter what the answer is, spending time to heal oneself can never hurt. Incorporating the extra power of crystals is a way to accelerate the results.