SUVAT Calculator

About the SUVAT Calculator

The five SUVAT equations describe motion under constant acceleration: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). Each equation relates four of the five variables, so knowing any three lets you solve for the other two. These equations are the foundation of classical kinematics and apply to everything from falling objects to braking cars.

The five equations are: v = u + at, s = ut + ½at², s = vt − ½at², v² = u² + 2as, and s = ½(u+v)t. In practice, you rarely need to memorize all five — they're derived from the first two plus the definition of acceleration. However, choosing the right equation matters because each omits one variable, and you should pick the equation that omits the variable you neither know nor need.

This calculator automatically selects the correct equation based on which three variables you provide. It shows the time-resolved velocity and displacement profile and overlays a reference table of all five SUVAT equations so you can verify the approach.

When This Page Helps

Use this calculator when a motion problem has constant acceleration and you want the missing displacement, velocity, acceleration, or time without juggling the equation choice yourself. It is useful for homework checks, quick engineering estimates, and sanity-checking worked solutions.

How to Use the Inputs

1. Identify which three of the five SUVAT variables (s, u, v, a, t) you know.
2. Enter those three values in the corresponding fields. Leave the other two blank.
3. The calculator will solve for the two unknown variables and show which equation was used.
4. Check the velocity profile chart and motion data table below.
5. Try different presets to explore common physics scenarios.

Example Calculation

Tips & Best Practices

• Use negative acceleration for deceleration (e.g., braking uses a = −(v²)/(2s)).
• Free fall uses a = 9.81 m/s² (or −9.81 if upward is positive).
• For vertical motion, define upward as positive: a projectile thrown up has u > 0, a = −9.81.
• These equations assume constant acceleration — they don't apply to circular motion or variable forces.
• If time is negative in the solution, the event occurred before t = 0 in your reference frame.

Choosing an Equation

Start with the three values you know, then pick the SUVAT form that excludes the unknown you do not want. That keeps the algebra short and reduces sign mistakes.

Interpretation

Negative acceleration is not automatically wrong; it usually means the object is slowing down or moving opposite to the chosen positive direction.

Frequently Asked Questions

• What does SUVAT stand for?

  It is a compact label for displacement, initial velocity, final velocity, acceleration, and time in constant-acceleration motion.

• Why are there five equations?

  Each equation leaves out one variable, so you can choose the form that matches the values you already know.

• Can I use these equations for projectile motion?

  Yes, if you split the motion into horizontal and vertical components and treat each one as a separate constant-acceleration problem.

• What if acceleration is not constant?

  Then the SUVAT equations are not valid. You need a calculus-based model for velocity and position.

• Is displacement the same as distance?

  No. Displacement has direction and can be negative; distance is the total path length and is always positive.

• Why do I sometimes get two solutions?

  Because the equations are often quadratic in time. One solution is usually the physically meaningful time you want.