What is the formula for velocity?

The core formula is v = d ÷ t (velocity equals distance over time). Rearranged, it also gives the other two quantities: d = v × t finds distance, and t = d ÷ v finds time. All three describe the same relationship.

What is the difference between speed and velocity?

Speed is how fast something moves — a scalar with only a magnitude. Velocity is speed in a specific direction — a vector with both magnitude and direction. Two cars at 50 mph have the same speed, but opposite velocities if they drive toward each other.

How do you find distance from velocity and time?

Rearrange v = d ÷ t into d = v × t, then multiply velocity by time. At 60 mph for 2 hours, distance = 60 × 2 = 120 miles. Make sure the time unit matches the velocity's time unit (hours with mph, seconds with m/s).

How do you find time from velocity and distance?

Rearrange v = d ÷ t into t = d ÷ v, then divide distance by velocity. Walking 5 km at 4 km/h takes 5 ÷ 4 = 1.25 hours, or 1 hour 15 minutes.

What units is velocity measured in?

Velocity is a length over a time, so any length-per-time pairing works. The SI unit is metres per second (m/s); kilometres per hour (km/h), miles per hour (mph), feet per second (ft/s) and knots are also common. Use the same length and time units you put in.

How do you convert m/s to mph?

Multiply metres per second by 2.23694 to get miles per hour. So 10 m/s × 2.23694 ≈ 22.37 mph. To go the other way, divide mph by 2.23694. The converter chart on this page does it for every common unit at once.

What is the difference between average and instantaneous velocity?

Average velocity uses the total displacement over the total time, so it smooths over any speeding up or slowing down. Instantaneous velocity is the velocity at a single moment — what a car's speedometer reads. This calculator finds average velocity.

How do you find final velocity with acceleration?

When motion is not steady, use the kinematic equation v = u + at: final velocity equals initial velocity plus acceleration times time. A car starting at 0 m/s and accelerating at 3 m/s² for 5 s reaches 0 + 3 × 5 = 15 m/s.

Physics

Velocity Calculator

Solve for velocity, distance, or time with v = distance ÷ time. Mix units freely — metres with seconds, miles with hours — see every step, and read the answer back in m/s, km/h, mph, ft/s, or knots.

Velocity calculator

v = d ÷ t

Solve for

Distance

Time

Velocity

Walking / cycling pace

The same speed, in every unit

m/s

km/h

mph

11.185

ft/s

16.404

knot

9.719

Updates as you type

Try an example

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The basics

What is velocity?

Velocity measures how quickly an object changes position — its displacement over time, in a given direction. Average velocity is simply the distance covered divided by the time it took. The same relationship rearranges three ways, which is why one formula answers three different questions.

v = d ÷ t

The core relationship

Velocity is distance over time. Divide how far something travelled by how long it took, and you get how fast it was going on average.

100 m ÷ 20 s = 5 m/s

speed vs velocity

Magnitude and direction

Speed is just the magnitude — how fast. Velocity adds a direction, making it a vector. A car going north at 30 mph and one going south at 30 mph share a speed but have opposite velocities.

Method

How to calculate velocity by hand

Four steps take you from a word problem to a number with the right units.

1
Identify what you know
Pull the distance and the time out of the problem, and note which one is the unknown you are solving for.
d = 100 m, t = 20 s, v = ?
2
Make the units consistent
Pick a length unit and a time unit and convert everything to match. Metres and seconds give m/s; miles and hours give mph.
metres + seconds → m/s
3
Apply the right form of the formula
Use v = d ÷ t for velocity, d = v × t for distance, or t = d ÷ v for time.
v = d ÷ t = 100 ÷ 20
4
Compute and label the answer
Do the arithmetic and attach the units — a number without units is not an answer in physics.
v = 5 m/s

Worked examples

See all three rearrangements

The same v = d ÷ t triangle, solved for each of its three quantities. Switch tabs to see the working laid out.

A runner covers 100 metres in 9.58 seconds. How fast is that?

Given d = 100 m t = 9.58 s

Formula v = d ÷ t

Substitute v = 100 ÷ 9.58

v ≈ 10.44 m/s (≈ 23.35 mph)

Concepts

Speed, velocity, and the cousins

These words get used loosely in everyday talk, but physics keeps them distinct. Knowing the difference is half of every kinematics question.

scalar

Speed

How fast, with no direction attached. It can never be negative, and it is the magnitude of the velocity.

50 mph — no direction

vector

Velocity

How fast and which way. Reversing direction flips its sign, even if the speed is unchanged.

50 mph due north

average

Average velocity

The overall rate across a whole trip. It ignores any speeding up or slowing down in between — only the endpoints matter.

total displacement ÷ total time

instantaneous

Instantaneous velocity

The velocity at one exact moment. As the time interval shrinks toward zero, average velocity becomes instantaneous velocity.

the speedometer reading

When motion changes

Final velocity with acceleration

When speed is not steady, v = d ÷ t gives only the average. To find the velocity at a moment during acceleration, reach for the kinematic equations.

v = u + a·t

From acceleration and time

Final velocity is the initial velocity u plus acceleration times the elapsed time.

v² = u² + 2·a·s

From acceleration and distance

When you know the distance s instead of the time, this form finds the final velocity directly.

v̄ = (u + v) ÷ 2

Average under constant acceleration

With steady acceleration, the average velocity is just the mean of the start and end velocities.

Where it shows up

Why velocity matters

The distance–time relationship underpins navigation, travel planning, sport, and every physics classroom.

ETA = d ÷ v

Travel and navigation

Sat-navs estimate arrival times by dividing the remaining distance by your current velocity — the same v = d ÷ t, rearranged.

splits

Sport and training

Pace is velocity in disguise. Runners and cyclists track it as minutes per mile or kilometres per hour to plan and compare efforts.

v = d ÷ t

Physics and engineering

From projectile motion to orbital mechanics, the velocity formula is the first tool out of the box for describing how things move.

Quick chart

Speed unit converter: m/s, km/h, mph, ft/s, knots

Enter any speed and read it in every unit at once — the fast answer to “what is X m/s in mph?” The reference table below shows the conversions for common round speeds.

Speed

m/s

km/h

mph

22.369

ft/s

32.808

knot

19.438

m/s	km/h	mph	ft/s	knot
1	3.6	2.24	3.28	1.94
5	18	11.18	16.4	9.72
10	36	22.37	32.81	19.44
15	54	33.55	49.21	29.16
20	72	44.74	65.62	38.88
25	90	55.92	82.02	48.6
30	108	67.11	98.43	58.32
50	180	111.85	164.04	97.19
100	360	223.69	328.08	194.38

Reference

How fast is that, really?

A velocity is easier to grasp next to something familiar. Here is where everyday speeds land on the scale.

Brisk walk

1.4 m/s

3 mph · 5 km/h

Bicycle (casual)

4.5 m/s

10 mph · 16 km/h

Usain Bolt (top)

12.4 m/s

28 mph · 45 km/h

City driving

13.4 m/s

30 mph · 48 km/h

Highway driving

29.1 m/s

65 mph · 105 km/h

Cheetah (sprint)

31 m/s

69 mph · 112 km/h

Commercial jet (cruise)

250 m/s

559 mph · 900 km/h

Speed of sound (air)

343 m/s

767 mph · 1,235 km/h

Worth knowing

Rules worth remembering

A handful of facts that keep velocity problems from going sideways.

units in = units out

Units propagate

Whatever length and time you feed in set the answer's units. Metres and seconds out give m/s; mix them up and the number is meaningless.

v = d ÷ t

One formula, three answers

You never memorise three formulas — only one, rearranged. Cover the quantity you want in the triangle and read off the rest.

displacement ≠ distance

Direction can cancel

Average velocity uses displacement, the straight-line change in position. A round trip back to the start has zero displacement, so zero average velocity.

t ≠ 0

Time can't be zero

Dividing by zero time is undefined — there is no velocity over no time. The calculator flags it rather than returning infinity.

sign = direction

Negative is allowed

A negative velocity simply means motion in the direction you chose as negative. Speed, its magnitude, never goes below zero.

average smooths

Average hides the detail

The same average velocity can come from steady cruising or from stopping and sprinting. To capture moment-to-moment motion you need instantaneous velocity.

Pitfalls

Common mistakes

Most wrong answers trace back to a few familiar slips. Watch for these.

mixed units

Forgetting to convert

Dividing miles by seconds, or kilometres by minutes, gives a number in an awkward unit. Settle on matching length and time units before you divide.

minutes as decimal

Treating 1 h 30 m as 1.30

An hour and a half is 1.5 hours, not 1.30. Convert minutes to a fraction of the larger unit before plugging in.

d vs v·t

Multiplying when you should divide

Solving for velocity is a division; solving for distance is a multiplication. Pick the form of the triangle that isolates your unknown.

average ≠ midpoint speed

Averaging two speeds wrongly

The average velocity of a there-and-back trip is not the mean of the two leg speeds — it uses total distance over total time, which can differ a lot.

FAQ

Common questions

Average velocity is the distance travelled divided by the time taken: v = d ÷ t. For 100 metres covered in 20 seconds, the velocity is 100 ÷ 20 = 5 m/s. Keep the length and time units consistent and the result is meaningful.

Keep going

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