Uniformly Accelerated Motion Calculator
Solve any constant-acceleration problem — the SUVAT equations, given any three of displacement, initial and final velocity, acceleration and time.
The standard constant-acceleration equations.
How the uniformly accelerated motion calculator works
Four equations describe constant acceleration, and each omits one variable: v = u + at (no s), s = ut + ½at² (no v), v² = u² + 2as (no t), and s = ½(u+v)t (no a).
Given any three of the five you can find the other two. The calculator takes u, a and t as the most common set and reports everything else.
Formula: v = u + at; s = ut + ½at²; v² = u² + 2as
Worked examples
| Inputs | Final velocity | Note |
|---|---|---|
| From rest at 3 m/s² for 5 s | 15 m/s | 15 m/s after 37.5 m |
| Braking from 20 m/s at −5 m/s² | 0 m/s | stops exactly at 4 s |
| Free fall for 3 s | 29.41995 m/s | 29.4 m/s after 44.1 m |
FAQFrequently asked questions
What does SUVAT stand for?
The five variables: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). Each equation uses four of them.
When do these equations apply?
Only when acceleration is constant. Variable acceleration needs calculus.
Which equation should I use?
The one that omits the variable you neither know nor want. If time is unknown, use v² = u² + 2as.
Why does displacement grow with t²?
Because the velocity itself is growing. Distance is the area under the velocity–time graph, and for a rising line that area is a triangle.
Does free fall use these?
Yes, with a = 9.81 m/s² downward — provided air resistance is negligible.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.