SUVAT Calculator
The SUVAT equations describe motion with constant acceleration using five quantities: displacement s, initial velocity u, final velocity v, acceleration a and time t. Enter any three and this calculator finds the other two, with the working.
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 GCSE Combined and Separate Science on this topic: worked steps, then exam-style questions with new numbers every time.
- Speed, distance and velocityForces and motionFree
- Acceleration and velocity-time graphsForces and motionPlus
- The equations of motionForces and motionPlus
See the whole courseThe full course, topic tests and mock papers come with Plus. See Plus
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.
- Known: u = 12 m/s, v = 30 m/s and t = 6 s. Wanted: a and s.
- v = u + at, so a = (30 − 12) / 6 = 3 m/s².
- 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.
About this tool
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.
Tips
- 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.