SUVAT calculator with working and graphs

A SUVAT calculator solves motion with constant acceleration. Give it any three of the five SUVAT values, s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time), and it finds the other two. Our SUVAT calculator also says which of the five equations it used for each unknown and why, gives both answers when an object passes the same point twice, and draws the velocity-time and displacement-time graphs.

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SUVAT Calculator

Solve any equation of motion from three known values

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How to use the SUVAT calculator

1. Open the SUVAT Calculator. It opens on u = 0, a = 2 m/s² and t = 5 s.
2. Under Known values, type exactly three of s, u, v, a and t, and leave the other two empty. Use negative numbers for anything pointing the other way.
3. Under Units, pick each kind of unit: mm, cm, m, km or miles for distance; m/s, km/s, km/h or mph for velocity; m/s², cm/s², ft/s² or g₀ for acceleration; seconds or hours for time.
4. Read all five values, with the found ones marked, the equation used for each and the working.
5. Switch the graph between Velocity-time, with the displacement shaded under the line, and Displacement-time. For practice, press Random problem.

With fewer than three values it asks for more; with four or five it asks you to clear the extra ones, because three always fix the rest.

The five SUVAT equations

Each equation leaves out one letter. To find an unknown, the calculator picks the equation that leaves out the other unknown, so it needs only the three values you gave. This is the same choice you make by hand, and it is the first thing the working explains. The SUVAT equations guide covers rearranging and deriving them.

Worked examples you can check in the calculator

Example 1: the opening values

u = 0, a = 2 m/s², t = 5 s. The unknowns are s and v. For s it uses the equation with no v, s = ut + ½at² = 0 + ½ × 2 × 5² = 25 m; for v, the one with no s, v = u + at = 0 + 2 × 5 = 10 m/s.

Example 2: speeds in mph

A car speeds up steadily from 30 mph to 70 mph in 8 s. Set the velocity unit to mph and type u = 30, v = 70 and t = 8. The calculator converts to 13.41 m/s and 31.29 m/s, then finds s = ½(u + v)t = 178.8 m and a = (v − u) ÷ t = 2.235 m/s².

Example 3: no time given

A train slows steadily from 25 m/s to a stop in 400 m. Type s = 400, u = 25 and v = 0. With t unknown, a comes from the equation without t, v² = u² + 2as:

The minus sign means it is slowing down. Then t = 2s ÷ (u + v) = 800 ÷ 25 = 32 s.

Example 4: two answers

A ball is thrown straight up at 15 m/s. When is it 10 m above where it was thrown? Take up as positive, so a = −9.81 m/s², and type s = 10, u = 15 and a = −9.81. First v² = 15² + 2 × (−9.81) × 10 = 28.8, so v = ±5.37 m/s. The calculator gives both solutions: t = 0.982 s on the way up, moving at +5.37 m/s, and t = 2.076 s on the way down, at −5.37 m/s. Both are marked on the graphs.

Example 5: an impossible question

Change u to 10 m/s. Now v² = 10² + 2 × (−9.81) × 10 = −96.2. A square can't be negative, and the calculator says so: the ball never reaches 10 m, because it stops and turns back first. A negative under the square root in v² = u² + 2as always means the object never gets that far.

Example 6: a dropped object

A stone is dropped from 45 m. Take down as positive: u = 0, a = 9.81 m/s², s = 45. Then v = √882.9 = 29.7 m/s and t = 3.03 s. The calculator also works out the negative root, −3.03 s, and rejects it, because time can't be negative.

Choosing the equation is the skill exams test. Try one, then press Mark to check your answer in the Laws of Motion course.

What the calculator doesn't do

• Changing acceleration. SUVAT only works when a is constant. Split a journey into stages of constant acceleration and solve each one, using the end of one stage as the start of the next.
• Two dimensions at once. For projectiles, solve the horizontal motion (a = 0) and the vertical motion (a = −9.81 m/s²) separately, linked by the same t.
• Air resistance. Falling objects are treated as accelerating at a constant g.

Common mistakes

• Mixing up directions. Choose a positive direction and stick to it; g is −9.81 m/s² if up is positive.
• Mixed units. km/h and m/s don't mix in an equation. Set the units, or convert first: divide km/h by 3.6.
• Assuming u = 0. Only when it starts from rest or is dropped.
• Ignoring the second answer. A quadratic in t can give two real times, and both can make sense.
• Using SUVAT when a changes. It gives the wrong answer for, say, a car whose acceleration falls as it speeds up.

Read next

Physics · MechanicsSUVAT equations (kinematic equations): all 5 with examplesAll 5 SUVAT equations, also called the kinematic equations, with a free calculator, worked examples, practice questions and what each exam gives you.