What does SUVAT stand for?

It is an acronym for the five quantities in the equations of motion: s is displacement, u is initial velocity, v is final velocity, a is acceleration and t is time. The letters come from the British physics syllabus, where the equations are usually introduced together. Some textbooks write the same relationships using x for displacement and v₀ for initial velocity, but the physics is identical.

What are the five SUVAT equations?

They are v = u + at, s = ut + ½at², s = vt − ½at², v² = u² + 2as, and s = ½(u + v)t. Each one deliberately leaves out a different variable — the first has no s, the second no v, the third no u, the fourth no t and the fifth no a. That omission is the key to choosing between them, and it is exactly what the panel on this page highlights for you.

How do I know which SUVAT equation to use?

Write down the three quantities you know and the one you want. The right equation is the one that contains all four — equivalently, the one that omits the quantity you neither know nor want. Since three knowns leave two unknowns, exactly two of the five equations apply to any well-posed problem, one for each unknown. That is a guarantee, not a rule of thumb, and it is why the panel always lights up precisely two.

Why do I need three values?

Because each equation links four of the five quantities, so knowing two leaves you one equation short. With three known, every remaining quantity is determined uniquely — or in a few cases, determined up to two possible times. Fewer than three and the problem is underspecified; more than three and you risk supplying an inconsistent set that no real motion could satisfy.

Can a SUVAT problem have two answers?

Yes, whenever the object turns around. Throw a ball upward at 20 m/s and it passes 15 m twice — at 0.99 seconds on the way up, travelling at 10.28 m/s, and again at 3.09 seconds on the way down at exactly −10.28 m/s. Both times satisfy s = ut + ½at², so both are correct; which one you want depends on the question. This calculator returns the earlier time and tells you explicitly when a second solution exists.

What is the difference between displacement and distance?

The s in SUVAT is displacement — the straight-line change in position from start to finish, carrying a sign. Distance is the total ground covered and is never negative. For motion in one direction they are the same. For a ball thrown up and caught again the displacement is zero while the distance is twice the peak height, so putting the distance into s would give a wrong answer.

How do I handle signs in SUVAT problems?

Choose one direction as positive before you start, then stay with it. Anything pointing the other way takes a minus sign. For a ball thrown upward with up as positive, u is positive, a is −9.81 m/s², and a displacement below the launch point is negative. Sign errors are the single commonest source of wrong SUVAT answers, and they usually show up as a negative time or an impossible square root.

Do the SUVAT equations work for falling objects?

Yes — free fall is just constant acceleration with a set to gravity, about 9.81 m/s² downward. Drop something from rest and u = 0, a = 9.81 and s is the drop height, which gives the fall time from s = ½at² and the landing speed from v² = 2as. Air resistance is ignored, so the figures are an upper bound; they are very close for dense compact objects over short drops.

When do the SUVAT equations stop working?

The moment the acceleration stops being constant. A car that accelerates hard, cruises, then brakes cannot be handled by one application of these equations — you must split it into three stages and apply them to each, carrying the final velocity of one stage into the next as the initial velocity of the following one. They also fail for circular motion, where the direction of acceleration changes continuously, and at speeds approaching light, where relativity takes over.

SUVAT Equations Calculator

Enter any three of s, u, v, a and t, and this calculator returns the other two — solving the five equations of motion the way an examiner expects. SUVAT is simply the initials of the five quantities that describe motion under constant acceleration: s for displacement, u for initial velocity, v for f...

s · u · v · a · t

Three values entered — solving for displacement and acceleration.

sDISPLACEMENT

solved: 120.701 m

uINITIAL SPEED

vFINAL SPEED

aACCELERATION

solved: 2.980 m/s²

tTIME

WORKED EXAMPLES

THE COMPLETE MOTION, IN SI UNITS

120.70

0.00

m/s

26.82

m/s

2.98

m/s²

9.00

Gold values were solved for; grey values are the ones you supplied.

ALL FIVE EQUATIONS CHECKED

eq 1

✓

eq 2

✓

eq 3

✓

eq 4

✓

eq 5

✓

Every equation balances with the solved values — the answer is self-consistent.

WHICH EQUATION DO I USE?

1v = u + a·tno sgives a

2s = u·t + ½a·t²no v

3s = v·t − ½a·t²no u

4v² = u² + 2a·sno t

5s = ½(u + v)·tno agives s

Each equation leaves one variable out. You know three, so two are unknown — and exactly two equations apply, the ones that omit s and a. Each of those contains your three knowns plus one unknown, so each hands you one answer.

SIMULATION

TIME

0.00 s

POSITION

0.0 m

SPEED

0.0 m/s

ACCEL

2.98 m/s²

What SUVAT assumes. Every one of these five equations holds only while the acceleration is constant. Change the acceleration part-way and you must split the journey into stages and apply the equations to each stage separately.

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type any three of the five values into the boxes. Known values get a solid black border; the two you leave blank are outlined in gold and will fill in once the third value is entered.
2
Pick units beside each field — metres, kilometres, miles or feet for displacement; m/s, km/h, mph, ft/s or knots for the velocities; m/s², ft/s² or g for acceleration; seconds, minutes or hours for time. Mixing units is safe because everything converts to SI first.
3
Look at the equation panel on the right. Exactly two of the five will be highlighted — the ones that apply to your particular problem — each labelled with the answer it produces. That is the step most students find hardest, done for you.
4
Check the five green ticks below the results. The calculator substitutes the completed set back into every equation and confirms each one balances, so you can be sure the answer is consistent rather than just arithmetically plausible.

THE FIVE EQUATIONS

Equation 1 — omits displacementv = u + a·t

Equation 2 — omits final speeds = u·t + ½a·t²

Equation 3 — omits initial speeds = v·t − ½a·t²

Equation 4 — omits timev² = u² + 2a·s

Equation 5 — omits accelerations = ½(u + v)·t

What the letters means u v a t

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Last updated: July 29, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.