SUVAT Calculator — Solve Any Kinematics Problem
The SUVAT calculator solves kinematics equations for uniformly accelerated motion. Enter any three of the five SUVAT variables and instantly find the remaining two. Supports both metric (SI) and US customary (imperial) units.
What Does SUVAT Stand For?
- s — Displacement (distance traveled in a straight line, in m or ft)
- u — Initial velocity (speed at the start, in m/s or ft/s)
- v — Final velocity (speed at the end, in m/s or ft/s)
- a — Acceleration (rate of change of velocity, in m/s² or ft/s²)
- t — Time (duration of motion, in seconds)
The Five SUVAT Formulas
These five equations completely describe any system undergoing uniform (constant) acceleration:
The SUVAT Formulas — Velocities
If you know the initial velocity u, final velocity v, and time t, acceleration a is simply:
a = (v − u) / t
Rearranging gives the first SUVAT equation: v = u + at.
The SUVAT Formulas — Displacement
Displacement equals the area under a velocity–time graph. For uniform acceleration that gives two equivalent forms:
- s = ut + ½at² (when u, a, t are known)
- s = ½(u + v)t (when u, v, t are known — the "average velocity" formula)
- v² = u² + 2as (when time is not available)
The SUVAT Formulas — Skipping Time
Equation 4, v² = u² + 2as, is especially useful because it relates velocity, acceleration, and displacement without time. For example, if you know a car brakes from 30 m/s to rest over 90 m, you can find a directly:
a = (v² − u²) / (2s) = (0 − 900) / 180 = −5 m/s²
How to Use This SUVAT Calculator
- Select your unit system (Metric or US Customary).
- Enter the values you know into any three of the five fields. Leave the other two blank.
- Click Calculate. The calculator automatically picks the correct SUVAT formula and solves for the two unknowns.
- Results appear instantly, along with the relevant equations verified with your numbers.
Metric vs. US Customary Units
| Variable | Metric (SI) | US Customary |
|---|---|---|
| Displacement (s) | meters (m) | feet (ft) |
| Initial / Final velocity (u, v) | m/s | ft/s |
| Acceleration (a) | m/s² | ft/s² |
| Time (t) | seconds (s) | seconds (s) |
Note: free-fall acceleration is 9.81 m/s² (metric) or 32.17 ft/s² (US customary).
Simple SUVAT Example Questions
Example 1 — Finding final velocity and displacement
A car starts from rest (u = 0 m/s) and accelerates at a = 3 m/s² for t = 10 s. Find v and s.
- v = u + at = 0 + 3 × 10 = 30 m/s
- s = ut + ½at² = 0 + ½ × 3 × 100 = 150 m
Example 2 — Finding time and acceleration (no time given)
A ball rolls from rest (u = 0) to v = 8 m/s over a distance of s = 16 m. Find a and t.
- a = (v² − u²) / (2s) = 64 / 32 = 2 m/s²
- t = (v − u) / a = 8 / 2 = 4 s
Example 3 — Braking distance (US units)
A car traveling at u = 88 ft/s brakes at a = −22 ft/s² until it stops (v = 0). Find braking distance s and time t.
- t = (v − u) / a = (0 − 88) / (−22) = 4 s
- s = ½(u + v)t = ½ × 88 × 4 = 176 ft
Frequently Asked Questions
When can I use SUVAT equations?
SUVAT equations apply whenever acceleration is constant (uniform). This covers free fall (ignoring air resistance), cars accelerating or braking on a straight road, projectiles (vertical component only), and many standard physics problems.
What if acceleration is not constant?
SUVAT equations do not apply to variable acceleration. You would need calculus (integration) or numerical methods instead.
Can displacement be negative?
Yes. Displacement is a vector: negative values mean motion in the opposite direction to the positive axis you chose. Distance is always positive; displacement can be negative.
Why are there five equations but only five variables?
Each equation omits one of the five variables, giving one equation for each possible "unknown variable." That's why knowing any three is always enough to solve the system.
Is this calculator suitable for GCSE and A-level physics?
Yes. The five SUVAT equations are core content for GCSE Physics (Higher) and A-level Mechanics. This calculator shows the equations alongside your results, making it useful for checking homework and understanding worked solutions.