About this calculator
SUVAT is the set of five equations for anything moving with constant acceleration: a car pulling away, a ball dropped from a bridge, a train braking into a station. The letters stand for displacement (s), initial speed (u), final speed (v), acceleration (a) and time (t).
Fill in any three of the five boxes and leave the other two blank. The calculator picks the right equation, works out the missing values and shows each step, so it doubles as a way to check your homework.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Dropped for 3 seconds (u = 0, a = 9.8, t = 3)
- Displacement (s)
- 44.1 m
- Initial speed (u)
- 0 m/s
- Final speed (v)
- 29.4 m/s
- Acceleration (a)
- 9.8 m/s²
- Time (t)
- 3 s
Given u = 0 m/s, a = 9.8 m/s², t = 3 s, the displacement is 44.1 m and the final speed is 29.4 m/s.
Show the working
- You know initial speed (u = 0), acceleration (a = 9.8), time (t = 3).
- Final speed: v = u + at = 0 + 9.8 × 3 = 29.4.
- Displacement: s = (u + v) ÷ 2 × t = (0 + 29.4) ÷ 2 × 3 = 44.1.
Car from rest to 20 m/s over 100 m
- Acceleration (a)
- 2 m/s²
- Displacement (s)
- 100 m
- Initial speed (u)
- 0 m/s
- Final speed (v)
- 20 m/s
- Time (t)
- 10 s
Given s = 100 m, u = 0 m/s, v = 20 m/s, the acceleration is 2 m/s² and the time is 10 s.
Show the working
- You know displacement (s = 100), initial speed (u = 0), final speed (v = 20).
- Time: t = 2s ÷ (u + v) = 2 × 100 ÷ (0 + 20) = 10.
- Acceleration: a = (v − u) ÷ t = (20 − 0) ÷ 10 = 2.
Cyclist: u = 5, a = 2, covers 50 m
- Final speed (v)
- 15 m/s
- Displacement (s)
- 50 m
- Initial speed (u)
- 5 m/s
- Acceleration (a)
- 2 m/s²
- Time (t)
- 5 s
Given s = 50 m, u = 5 m/s, a = 2 m/s², the final speed is 15 m/s and the time is 5 s.
Show the working
- You know displacement (s = 50), initial speed (u = 5), acceleration (a = 2).
- Final speed: v = ±√(u² + 2as) = ±√(5² + 2 × 2 × 50) (taking the direction of travel) = 15.
- Time: t = (v − u) ÷ a = (15 − 5) ÷ 2 = 5.
Train braking: 10 to 20 m/s in 5 s
- Displacement (s)
- 75 m
- Initial speed (u)
- 10 m/s
- Final speed (v)
- 20 m/s
- Acceleration (a)
- 2 m/s²
- Time (t)
- 5 s
Given u = 10 m/s, v = 20 m/s, t = 5 s, the displacement is 75 m and the acceleration is 2 m/s².
Show the working
- You know initial speed (u = 10), final speed (v = 20), time (t = 5).
- Acceleration: a = (v − u) ÷ t = (20 − 10) ÷ 5 = 2.
- Displacement: s = (u + v) ÷ 2 × t = (10 + 20) ÷ 2 × 5 = 75.
The five SUVAT equations
- v = u + at (no displacement)
- s = ½ (u + v) t (no acceleration)
- s = ut + ½ a t² (no final speed)
- s = vt − ½ a t² (no initial speed)
- v² = u² + 2as (no time)
Each equation leaves out one of the five quantities, which is why any three known values are enough: there is always an equation containing your three knowns and one unknown.
When SUVAT applies
SUVAT only works when the acceleration is constant and the motion is in a straight line. Free fall near the Earth's surface qualifies (g is about 9.81 m/s² downwards, ignoring air resistance). A car accelerating with the pedal changing, or a rocket burning fuel, does not.
Choose one direction as positive and stick to it. If you throw a ball upwards and call up positive, then gravity is −9.81 m/s².
Two answers and the turning point
Some problems have two valid answers. A ball thrown upwards passes the same height twice, once going up and once coming down. When that happens the calculator gives the first pass and adds a note with the second solution. Negative time answers are rejected because they describe the past.
Frequently asked questions
What does SUVAT stand for?
Displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). The name is just those letters.
How many values do I need to enter?
Exactly three. With fewer the problem has many answers, and with more the extra values may contradict each other.
Can I use feet or miles per hour?
Yes, as long as you use the same system throughout. The labels say metres and seconds, but the equations work in any consistent units.
What value of g should I use?
Use 9.81 m/s² (9.80665 is the standard value). Use −9.81 if you have chosen up as the positive direction.
Why did it say 'no real answer'?
Because the numbers describe something that cannot happen, for example an object that is slowing down and never reaches the displacement you entered.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.