SUVAT calculator

Fill in any three of s, u, v, a and t. This works out the rest, and more importantly tells you which equation it picked and why that one, which is the part students actually get stuck on.

s · displacement (m)

u · initial velocity (m/s)

v · final velocity (m/s)

a · acceleration (m/s²)

t · time (s)

Leave the two you are solving for blank. Use a negative value for anything pointing the opposite way to your chosen positive direction, including deceleration.

The five equations, and when each one is the right pick

There are five SUVAT equations and each one leaves out exactly one variable. That is the whole trick to choosing between them. Work out which quantity you neither know nor want, then use the equation that does not contain it.

Equation	Leaves out	Use it when
v = u + at	s	Displacement is not involved
s = ut + ½at²	v	You do not know or need final velocity
s = ½(u + v)t	a	Acceleration is unknown or irrelevant
v² = u² + 2as	t	Time is not given and not asked for
s = vt − ½at²	u	You do not know the starting velocity

The mistake that costs the most marks: signs. Pick a positive direction at the start and stick to it for the whole question. If up is positive, gravity is −9.81 m/s², a ball thrown upward has positive u, and a displacement below the starting point comes out negative. Mixing signs mid-question is the single most common source of wrong answers here.

What SUVAT can and cannot do

These equations only work when acceleration is constant. That covers most school problems: objects falling under gravity, cars braking steadily, trolleys on a ramp. It does not cover situations where the acceleration changes as you go, such as air resistance building up as something speeds up, or a spring where the force depends on how far it is stretched.

They also work in one dimension at a time. For projectile motion you split the problem into horizontal and vertical parts and run SUVAT separately on each, with the two linked by the shared time.

Common questions

Why is it called SUVAT?: It is just the five symbols: s for displacement, u for initial velocity, v for final velocity, a for acceleration, t for time. Some countries use different letters, such as v₀ for initial velocity and v for final in US textbooks, or x instead of s for displacement. The equations are identical.
Should I use 9.8, 9.81 or 10 for gravity?: Check your exam board's data sheet. UK A-Level typically uses 9.81 m/s², GCSE often uses 9.8, and some courses use 10 to keep the arithmetic simple. This calculator defaults to 9.8, which GCSE, AP, HSC, VCE and CBSE all use. UK A-level specifies 9.81, so change it if that is your syllabus.
What is the difference between displacement and distance?: Displacement is straight-line change in position, including direction, so it can be negative. Distance is total path travelled and is always positive. A ball thrown up and caught again has zero displacement but has travelled a real distance. SUVAT works with displacement.
Why did I get two answers for time?: Because s = ut + ½at² is a quadratic, and a projectile can pass the same height twice, once going up and once coming down. Both are mathematically valid. Pick the one that fits the situation, and discard any negative time.