Velocity Formula: v = s/t, SI Unit, Examples and Calculator

The velocity formula is $v = \frac{s}{t}$ : divide the displacement of an object by the time it took, and keep the direction. A car that ends up 300 m north of where it started after 20 s has a velocity of 15 m/s north. The direction is part of the answer, and that is the single idea that separates velocity from speed.

In Indian books s stands for displacement, so the formula reads v = s/t. US books usually write $v = \frac{\Delta x}{\Delta t}$ , where $\Delta x$ is the change in position along a line. Both say the same thing. Velocity is the starting point of the kinematics formulas chapter, and every equation of motion is built on it.

Quick facts

Formula
$v = \frac{s}{t}$ or $v = \frac{\Delta x}{\Delta t}$
SI unit
metre per second (m/s)
Dimensional formula
[M⁰ L¹ T⁻¹]
Type
Vector: size plus direction
Can it be negative
Yes, a minus sign means motion opposite to the chosen positive direction
Size of velocity
Called speed when you drop the direction

What the formula for velocity means, symbol by symbol

Symbols in v = s / t
Symbol	Quantity	SI unit	Notes
$v$	Velocity	m/s	Carries a direction, such as east or a plus or minus sign
$s$ or $\Delta x$	Displacement	m	Final position minus initial position, a straight line from start to finish
$t$ or $\Delta t$	Time taken	s	Always positive

The top of the fraction is displacement, not the path length. If you walk 30 m east and then 10 m back west, your displacement is 20 m east even though your feet covered 40 m. Put 20 m into the formula, not 40 m. When the motion is along a straight line with no turning back, the two numbers match and velocity and speed have the same size.

Because time is always positive, the sign of v always follows the sign of s. Moving toward your positive direction gives a positive velocity, and moving away from it gives a negative one.

What is the formula to calculate velocity? Four steps

Fix a positive direction. Write it down, for example east is positive or up is positive.
Find the displacement. Take final position minus starting position, with its sign. Ignore any back and forth in between.
Put everything in SI units. Kilometres become metres (times 1000) and minutes become seconds (times 60).
Divide and state the direction. Write the number, the unit m/s and the direction or sign together.

The same formula to find velocity is built into the velocity formula calculator on this page. Enter any two of velocity, displacement and time in SI units and it returns the third, which is a fast way to check homework.

Velocity formula examples

Example 1: a scooter on a straight road

A delivery scooter moves 600 m east along a straight road in 50 s. What is its velocity?

Given: s = 600 m east, t = 50 s.

$v = \frac{600\ \text{m}}{50\ \text{s}} = 12\ \text{m/s}$

Answer: 12 m/s east.

Example 2: a train, with a unit conversion

A train travels 45 km due north in 30 minutes on straight track. Find its velocity in m/s.

Convert: s = 45 × 1000 = 45 000 m, t = 30 × 60 = 1800 s.

$v = \frac{45\,000}{1800} = 25\ \text{m/s}$

Answer: 25 m/s north, which is the same as 90 km/h north.

Example 3: a negative velocity

A toy car moves along a number line from x = 2 m to x = −4 m in 3 s. Find its velocity.

$v = \frac{x_2 - x_1}{t} = \frac{-4 - 2}{3} = -2\ \text{m/s}$

The minus sign tells you the car moved toward smaller x. Its speed is 2 m/s.

An athlete who jogs once around a 400 m oval ends where she began, so the displacement is zero and the velocity for the lap is zero, even though the speed was not.

Other velocity formulas in physics

The basic fraction is the definition. Questions often give other quantities, so these related forms are worth knowing:

Velocity formulas and when each one applies
Situation	Formula	Page
Over a whole trip	$v_{avg} = \frac{\Delta x}{\Delta t}$	Average velocity
At one instant	$v = \frac{dx}{dt}$	Instantaneous velocity
Constant acceleration, time known	$v = u + at$	Final velocity
Constant acceleration, distance known	$v^2 = u^2 + 2as$	Constant acceleration
Motion on a circle	$v = \omega r$	Linear velocity
Seen from a moving observer	$v_{AB} = v_A - v_B$	Relative velocity

The two constant acceleration rows need a steady acceleration, as in free fall or a car braking evenly. The definition in the first row works for any motion, but it gives the average value over the time interval.

Velocity and speed compared

Velocity versus speed
Feature	Velocity	Speed
Formula	$\frac{\text{displacement}}{\text{time}}$	$\frac{\text{distance}}{\text{time}}$
Scalar or vector	Vector	Scalar
Can be negative	Yes	No
One lap of a circular track	Zero on average	Positive
SI unit	m/s	m/s

Both share a unit, which is why students mix them up. When a question says “velocity”, the examiner expects a direction in the answer. See the speed formula page for the scalar version, and the displacement formula page for how to get s when the path bends.

Units, dimensions and the position time graph

Velocity is metres divided by seconds, so its SI unit is m/s. Other units you will see are km/h and cm/s. Going from km/h to m/s means dividing by 3.6; the reverse trip multiplies by 3.6. In base dimensions velocity is length per time, giving [M⁰ L¹ T⁻¹]; a line by line working appears on the dimensional formula of velocity page.

On a position time graph, velocity is the slope. A straight sloping line means the velocity is constant. A steeper line means a faster object. A line sloping downward means a negative velocity, and a flat line means the object is at rest. If the line curves, the slope of the tangent at a point gives the velocity at that moment.

Mistakes students make with velocity

Using total distance instead of displacement. If the path turns back, the two are different. Only displacement goes in the velocity formula.
Leaving out the direction. “12 m/s” answers a speed question. “12 m/s east” answers a velocity question.
Forgetting to convert. Dividing kilometres by minutes gives km/min, which is rarely what the question wants.
Averaging two velocities. Adding two velocities and halving them only works when equal times are spent at each value, not equal distances.

Sense check: walking pace is about 1.4 m/s and a fast car on a highway is about 30 m/s. An answer for a cyclist above 100 m/s means a unit slipped.

Frequently asked questions

What's the formula for velocity in physics?

Velocity equals displacement divided by time, v = s / t, with the direction of the displacement. US books often write v = Δx / Δt, which is the same idea.

Which SI unit does velocity use?

Velocity is measured in metres per second (m/s) in SI. Kilometres per hour are common in everyday life, and 1 m/s equals 3.6 km/h.

Is velocity a vector quantity?

Yes. Velocity has a size and a direction, so two cars at 20 m/s going opposite ways have different velocities. Speed is the size of velocity without the direction.

What is the velocity formula for Class 9?

In Class 9 the formula is velocity = displacement / time. You also meet v = u + at, the first equation of motion, for an object with uniform acceleration.

How do you calculate velocity when acceleration is given?

Use the first equation of motion, v = u + at, where u is the starting velocity, a the acceleration and t the time. If time is not given but distance is, use v² = u² + 2as.