SUVAT Calculator: Straight-Line Motion with Constant Acceleration

Final speed and distance travelled from the starting speed, acceleration and time.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

When an object moves in a straight line with constant acceleration a, the speed after a time t is v = u + a t and the distance is s = u t + ½ a t². These are two of the five SUVAT equations.

Use a negative acceleration for slowing down. Gravity is 9.81 m/s² downward. The equations do not apply if the acceleration changes during the motion.

Formulas used

  • v = u + a t
  • s = u t + \tfrac{1}{2} a t^2
  • v^2 = u^2 + 2 a s

Worked example

With the default numbers in the calculator above:

  1. Final speed: 10 m/s
  2. Distance travelled: 25 m
  3. Average speed: 5 m/s
  4. Check with the third equation: both sides agree

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What do the letters stand for?

s is the distance (displacement), u the starting speed, v the final speed, a the acceleration and t the time.

What if the acceleration is not constant?

Then you need calculus: integrate the acceleration over time to get the speed and again to get the distance.

Can I use it for a falling object?

Yes, with a = 9.81 m/s² when you take down as positive, ignoring air resistance.

Related calculators

Further reading: Meriam and Kraige, Engineering Mechanics: Dynamics; Hibbeler, Engineering Mechanics: Dynamics; Rao, Mechanical Vibrations.

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