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Saiyans have various transformations.
Requirements
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Great Ape - Any Power level Need a full moon.
FSSJ - Power-level 38 mil+
SSJ - Power-level 95 mil+ Need to be pure hearted.
ASSJ - Power-level 110 mil+
USSJ - Power-level 125 mil+
FPSSJ - Power-level 140 mil+ Need to master SSJ.
SSJ2 - Power-level 150 mil+
LSSJ - Power-level 250 mil+ An anomaly.
FPSSJ2 - Power level 250 mil+ Need to master SSJ2.
SSJ3 - Power-level 300 mil+ Need a good mastery of Ki.
SSJ4 - Power-level 500 mil+ Need to be a Golden Ôozaru.
SSJG/SSJR - Power-level 750+ Need 6 pure hearted Saiyans.
SBG - Power-level 750+ Need to absorb Godly Ki or run out of time as a SSJG.
SSJGSSJ/SSJB - Power-level 1 bil+ Need to have/be near God energy.
- ASSJ and USSJ are forceful and waste energy.
Multipliers
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Great Ape - x10
FSSJ - x20
SSJ - x50
ASSJ - x75
USSJ - x87.5
FPSSJ - x50 Because it is just mastered SSJ however better fighting in general
SSJ2 - x100
LSSJ - x100 it's basically SSJ2 but green.
FPSSJ2 - x100 Because it is just mastered SSJ2 however better fighting in general
SSJ3 - x400
SSJ4 - x1600
SSJG/SSJR - x50000
SBG - x50000 Since it's basically base of SSJB.
SSJGSSJ/SSJB - x2500000 Its basically the SSJ of SSJG.
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Transformation Descriptions
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GIANT APEb大猿(Ôozaru): Saiyans that still have their tails have the ability to transform into "giant monkeys," a form called Ôozaru. However, a full moon is needed to begin the process or an equal substitute, such as the well known Saiyan "Power Ball" technique. The Multiplier for Ôozaru is 10x the user's base.
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QUASI-SUPERSAIYAN 疑似超サイヤ人(FSSJ): One of the most interesting stages to appear is actually one that stems from a single movie, placing it outside of the normal, canon continuity. Since at the time Goku could only reach Kaioken x 20 and it is believed that FSSJ looks and is a glorified Kaioken. It can almost be seen as a Continuous Kaioken therefore its multiplier would be 20x the user's base.
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SUPER SAIYAN 超サイヤ人(SSJ1): The stage is characterized by giant spiky golden hair. The pupils also turn a bluish green color. The power of the character is exponentially increased. Control over this power is not always the easiest thing at first. The multiplier for this form is confirmed to be x50.
While a high power level, intense rage, and a need for more power are all stated requirements for an initial Super Saiyan transformation, exhaustion also seems to play a role.
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"ULTRA" or "BEYOND" SUPER SAIYAN 超サイヤ人第2段階(USSJ): There are actually two stages within the "USSJ" stage, just varying levels of the same exact thing. In the first stage, the muscles increase in size, while power rises. In the second stage, the muscles increase in size even more, the power rises even more, speed falls, and with some characters, the pupils disappear. In each of the those stages, more energy is consumed, as well. Stage 1 of USSJ "Super Saiyan Grade II" also known as "Ascended Super Saiyan" 超サイヤ人第3段階(ASSJ) is a form is in-between USSJ1 and Initial SSJ1. Stage 2 of USSJ "Super Saiyan Grade III" also known as "Ultra Super Saiyan" is between USSJ1 and SSJ2 - it doesn't have the speed of SSJ2. The ASSJ Multiplier is 75x Base, and the USSJ multiplier is 87.5x Base.
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FULL-POWER SUPER SAIYAN 超サイヤ人フルパワー(FPSSJ): Full Power Super Saiyan is a relaxed form of Super Saiyan, it is more natural than the others. It allows the user to power up in the already achieved Super Saiyan Form. This allows them to have extra energy during a fight. Since FPSSJ is more calm it allows the user to concentrate allowing them to dodge and attack easier.
It is not a separate form but it allows you to use SSJ's maximum potential.
It can also be possible for SSJ2...
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SUPER SAIYAN 2 超サイヤ人 ツー(SSJ2): The direct successor to the first Super Saiyan transformation. It is very similar to the original form in appearance and attainment; however, the power output is far greater, as speed, strength, and energy output all drastically increase. It is SSJ x 2 so it is BASE PL X 100.
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LEGENDARY SUPER SAIYAN 伝説の超サイヤ人(LSSJ): Similar to Super Saiyan 2, Legendary Super Saiyan increases speed, strength, and energy. However, strength isn't just increased, it exponentially enlarges. Thus the user will have extraordinarily large muscles. The user would go completely out of control as shown in the movies Broly the Legendary Super Saiyan, Broly Second Coming, and Bio-Broly. However, they leave themselves open while punching, allowing them to be attacked mid-punch. However, attacks dealt may not do much damage since defence is one of the abnormal stats that this form has.
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SUPER SAIYAN 3 超サイヤ人スリー(SSJ3): The third form of Super Saiyan, the successor to the first and second transformations. The form uses a Saiyan's full potential with power extracted from every drop of their blood. Where the third stage of Super Saiyan's purpose was 100% utilization of physical stamina, the purpose of the Super Saiyan 3 transformation is to increase the utilization of ki, and as a result, the transformation rapidly consumes the energy of the user. This notably leads to extended levels of fatigue, even long after powering down. The Multiplier for SSJ3 is confirmed to be 400x Base as it is SSJ 2 X 4.
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SUPER SAIYAN RED/SUPER SAIYAN GOD 超サイヤ人ゴッド(SSJR/SSJG): SSJG is so powerful that your energy can't be sensed in the form. This form also allows the user to sense godly ki. It is powerful however the form drains the user's energy reserves fairly quickly, thus creating a time limit. However, the user can become what is known as 'SAIYAN BEYOND GOD' (SBG) which is basically their base but at a godly level. Goku achieved this right after his Super Saiyan God ran out.
This stage can be skipped to go straight to the SSJB level. This was shown by Vegeta in RoF. SSJG, however, can be accessed if the user becomes a SBG. You can achieve SBG by absorbing God Ki. Vegeta did this while training with Whis and Goku.
SSJG is basically a power up. It increases the user's power exponentially.
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SUPER SAIYAN BLUE/SUPER SAIYAN GOD SUPER SAIYAN 超サイヤ人ブルー(SSJB/SSJGSSJ): This form is attained by controlling godly Ki. Goku and Vegeta gained this by holding in their Ki so that it doesn't leak. That allowed them to absorb the godly energy of Berus' planet.
SSJB is much more powerful than SSJG. Super Saiyan Blue is a permanent transformation as seen by Goku and Vegeta transforming into this form during their battle with Frieza in the movie Dragon Ball Resurrection F. Since it's basically the God level of SSJ, it's multiplier is x50 compared to SBG.
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NON CANON FORMS [but noted]
Super Saiyan 4 超サイヤ人フォー(SSJ4): This form is the direct successor to Super Saiyan Three. The only way a Saiyan can attain Super Saiyan 4 is if they can already turn Super Saiyan, transforms into a Golden Great Ape, and then regains conscious control over the form. After this form is attained once, it can be accessed at any point as shown in the Non-Canon American series, Dragon Ball Grand Tours. The Multiplier for SSJ4 is 4x Super Saiyan Three making it 1600x Base.
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