Mechanics⏱ 4 min read

Speed Formula

s = d / t

What is the Speed Formula?

Speed describes how much distance an object covers per unit of time. It's a scalar quantity — it has a magnitude but no direction, which distinguishes it from velocity (the same idea, but with direction included, and capable of being negative depending on which way something is defined as moving).

The units of speed always come from dividing a distance unit by a time unit — meters per second, kilometers per hour, and miles per hour are all speed units built exactly this way, which is a useful sanity check: if a calculated "speed" doesn't come out in distance-per-time units, something went wrong in the setup.

This formula as written gives average speed over an entire trip — total distance divided by total time — which can be quite different from an object's instantaneous speed at any one moment (a car's speedometer reading right now, versus its average speed including every red light on a 2-hour drive). When a problem needs the speed at one specific instant rather than an overall average, that's a calculus concept (a derivative of position with respect to time), not something this formula alone captures.

What Each Variable Means

SpeedHow fast the object is moving. (m/s, km/h, or mph)

DistanceThe total length of the path traveled. (meters, km, or miles)

TimeHow long the journey takes. (seconds or hours)

Units

Quantity	Symbol	Unit
Speed	`s`	meters per second (m/s)
Distance	`d`	meters (m)
Time	`t`	seconds (s)

When to Use It

Finding how fast something is moving, given the distance and time
Finding the distance covered, given speed and time
Finding how long a journey takes, given distance and speed

Step-by-Step Example

Problem: A car travels 150 km in 2 hours. What is its speed?

Write down the known values

Identify distance and time.

d = 150 km, t = 2 h

Apply the formula

Divide distance by time.

s = 150 / 2

✓

Answer: s = 75 km/h

Interactive Calculator

d (distance)t (time)

Result will appear here

Solving for Other Variables

d = s × tSolve for distance when speed and time are known.

t = d / sSolve for time when distance and speed are known.

Common Mistakes

Mistake: Mixing units, like distance in km with time in minutes.
Fix: Convert to consistent units before dividing — either both to the same time scale, or convert the final answer explicitly.
Mistake: Confusing speed with velocity.
Fix: Speed is just magnitude (a number). Velocity is the same idea but includes direction, and can be negative if direction is taken into account.

Practice Questions

A cyclist travels 30 km in 1.5 hours. What is their speed?
A runner moves at 5 m/s for 40 seconds. How far do they travel?
Hint: Use the rearranged formula d = s × t.

Frequently Asked Questions

What's the fastest speed possible?

The speed of light in a vacuum, approximately 299,792,458 m/s — nothing with mass can reach or exceed it.

Is average speed the same as instantaneous speed?

No — average speed is total distance over total time for an entire trip, while instantaneous speed is how fast something is moving at one specific moment, which can vary throughout the trip.