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Brainlag

SUVAT calculator

Enter any three of s, u, v, a and t and get the other two, with the equation of motion used and the working shown. For GCSE and A-level physics and A-level maths mechanics.

m

m/s

m/s

m/s²

s

Take one direction as positive. For something thrown upwards, up is positive and a = −9.81 m/s².

See it happen: Projectile motion

Learn this properly

Lessons from the Combined and Separate Science courses on this topic: worked steps, then exam-style questions with new numbers every time.

See the whole course

Formulas

  • v = u + at
  • s = ut + ½at2
  • s = vt − ½at2
  • v2 = u2 + 2as
  • s = ½(u + v)t

Worked example

A car speeds up from 12 m/s to 30 m/s in 6 s. Find its acceleration and the distance it covers.

  1. Known: u = 12 m/s, v = 30 m/s and t = 6 s. Wanted: a and s.
  2. v = u + at, so a = (30 − 12) / 6 = 3 m/s2.
  3. s = ½(u + v)t = ½ × (12 + 30) × 6 = 126 m.

Answer: a = 3 m/s2 and s = 126 m.

Common mistakes

  • Mixing units: change km/h to m/s (divide by 3.6) and minutes to seconds first.
  • Losing the sign of g: with up as positive, a = −9.81 m/s2 on the way up and on the way down.
  • Setting the whole velocity to 0 at the top of a throw: only the vertical part is 0 there.
  • Using SUVAT when the acceleration changes, for example with air resistance that grows with speed.

How it works

This SUVAT calculator solves motion problems with constant acceleration. Fill in any three of displacement s, initial velocity u, final velocity v, acceleration a and time t, and it works out the other two. It tells you which equation it used and shows the numbers substituted in, so you can see how the answer was reached and copy the method into your own working.

  1. List what the question gives you and what it asks for. Write each value in SI units: metres, m/s, m/s2 and seconds.
  2. Enter any three of s, u, v, a and t. Leave the other two empty.
  3. Read the two answers, the equation used and the substitution with your numbers.
  4. If two answers are possible, both are shown, for example two times at which a ball passes the same height, or v = ± a value. Pick the one that fits the situation.

Tips

  • For free fall, take up as positive and use a = -9.81 m/s2. A ball thrown up at u = 20 m/s reaches its highest point (v = 0) at s = 20.39 m.
  • The five equations: v = u + at, s = ut + ½at2, s = vt - ½at2, v2 = u2 + 2as and s = ½(u + v)t. Each one leaves out one of the five quantities.
  • Starting from rest means u = 0. Coming to a stop means v = 0. Dropped means u = 0, with a = -9.81 m/s2 if up is positive.
  • Signs carry direction. A negative displacement means the object ends up below or behind where it started, which is often correct.

FAQ

What does SUVAT stand for?
The five quantities in the equations of motion for constant acceleration: s displacement (m), u initial velocity (m/s), v final velocity (m/s), a acceleration (m/s2) and t time (s). Each of the five equations leaves one of them out, so pick the one without the quantity you neither know nor need.
When can you use the SUVAT equations?
Only when the acceleration is constant, for example an object in free fall (a = 9.8 m/s2 downwards, ignoring air resistance) or a car braking evenly. If the acceleration changes, use a velocity-time graph or calculus instead.
Which equation does it choose?
The one that links your three known values with the unknown you need. If you know u, a and t, it uses v = u + at for v and s = ut + ½at2 for s. The working names the equation each time.
Why does it say my inputs are impossible?
Some combinations cannot happen with constant acceleration, such as a negative number under a square root in v2 = u2 + 2as, or a time that comes out negative. Check the signs of your values and the direction you chose as positive.
Can I use km/h?
Convert to m/s first by dividing by 3.6, so 72 km/h becomes 20 m/s. The calculator works in SI units, and mixing units gives wrong answers.

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