Working / steps
Equations used
Checks
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SUVAT equations explained
SUVAT is a set of equations of motion used for straight‑line kinematics when acceleration is constant (uniform). If the acceleration changes during the motion, SUVAT is not suitable.
In GCSE Physics, A‑level Physics and mechanics, you typically know at least 3 of the 5 variables and use SUVAT to find the others. This calculator converts common UK units (including mph) into SI, shows clear working, and highlights physically sensible solutions.
- s — displacement (m)
- u — initial velocity (m/s)
- v — final velocity (m/s)
- a — acceleration (m/s²)
- t — time taken (s)
The 5 SUVAT equations
- v = u + at
- s = ut + ½at2
- s = vt − ½at2
- v2 = u2 + 2as
- s = (u + v)t / 2
SUVAT FAQ (GCSE & A‑level)
How many values do I need to use SUVAT?
You normally need at least 3 of the 5 variables (s, u, v, a, t). With 3 known values, you can usually calculate the other 2. With four known values, you can calculate the last one and also run a consistency check.
When should I NOT use SUVAT?
Do not use SUVAT if acceleration is not constant (for example: changing thrust, varying friction, or air resistance that matters). In those cases you may need graphs, calculus, or numerical methods.
What’s the difference between distance and displacement?
Distance is how far you travelled in total. Displacement is the change in position in a chosen direction, so it can be negative. SUVAT uses displacement (s).
Why do I sometimes get 2 answers for time?
Some SUVAT rearrangements form a quadratic, giving 2 mathematical solutions. In exams you typically choose the physically valid one (often the positive time). For projectiles you can sometimes have 2 positive times (going up and coming down).
What sign convention should I use for vertical motion?
Choose a positive direction and stick to it. A common GCSE/A‑level choice is “upwards positive”, which makes free‑fall acceleration a = −g. If you choose “downwards positive”, free‑fall acceleration is a = +g.
Can I use mph in SUVAT?
Yes, you just must be consistent. This calculator converts mph to m/s internally and shows the SI conversion in the working.
What value of g should I use in the UK?
Many mark schemes accept g = 9.8 m/s², while more precise work uses 9.81 m/s². If you use g, make sure the sign matches your chosen positive direction.
How do I model braking or stopping distance with SUVAT?
Braking is usually constant (negative) acceleration over a time or distance. If you know initial speed and stopping distance, you can use v² = u² + 2as with v = 0 to find a, then find time if needed.
My answers look wrong, what are the most common mistakes?
Common issues are mixing units (mph with m/s), forgetting to convert minutes to seconds, using distance instead of displacement, or getting signs wrong (e.g., using +g with “upwards positive”).
What does “constant acceleration” mean in simple terms?
It means the acceleration does not change during the motion, so velocity changes by equal amounts in equal time intervals. The velocity–time graph is a straight line.
Does SUVAT work for motion in 2 dimensions?
Not directly. For projectiles, you apply SUVAT separately in the horizontal and vertical directions (with different accelerations), using the same time t in both.
How can I get more method marks in GCSE/A‑level questions?
Write down the SUVAT equation you’re using, substitute values with correct signs and SI units, and show the rearrangement before the final numerical answer. The working section is designed to mirror that style.