Calculating
Speed
How fast? How far? How long? Every one of those questions comes from a single, friendly formula — and by the end of this lesson you'll use it without thinking.
Speed is everywhere you look
🚦 On the road
Speed limits, travel time, fuel stops, "are we there yet?" — all speed calculations.
🏃 In sport
A sprinter's pace, a bowler's delivery, your PB on a 5 km run — measured as speed.
✈️ Getting around
Flights, trains and deliveries are all planned using distance, time and speed.
So, what is speed?
Speed is a rate
It tells you how much distance is covered in a given amount of time. It answers: in one hour (or one second), how far do you go?
A car at 80 km/h covers 80 kilometres every hour. A sprinter at 10 m/s covers 10 metres every second.
Distance divided by the time it took.
That's the whole idea.
Three quantities, three units
| Quantity | Symbol | Common units |
|---|---|---|
| Distance — how far | d | metres (m), kilometres (km) |
| Time — how long | t | seconds (s), hours (h) |
| Speed — how fast | s | m/s, km/h |
Speed = distance ÷ time
The D S T formula triangle
How to use it
Cover the letter you want to find — what's left shows the calculation.
Finding speed s = d ÷ t
The question
A car travels 240 km in 3 hours. What is its average speed?
s = d ÷ t
s = 240 ÷ 3
s = 80 km/h
Finding distance d = s × t
The question
A cyclist rides at a steady 18 km/h for 2.5 hours. How far do they travel?
d = s × t
d = 18 × 2.5
d = 45 km
Finding time t = d ÷ s
The question
A train covers 300 km at a steady speed of 100 km/h. How long does the trip take?
t = d ÷ s
t = 300 ÷ 100
t = 3 hours
km/h vs m/s
🚗 Kilometres per hour
Everyday travel: cars, buses, road signs, long journeys.
🏃 Metres per second
Science, sport and short bursts: sprinters, falling objects, physics.
km/h → m/s ÷ 3.6
The rule
Going to the smaller unit (m/s), the number gets smaller — so we divide by 3.6.
Example
Convert 90 km/h to m/s.
m/s → km/h × 3.6
The rule
Going to the bigger unit (km/h), the number gets bigger — so we multiply by 3.6.
Example
Convert 12 m/s to km/h.
Average speed
Real trips speed up and slow down.
Average speed smooths the whole journey into one number.
Add up first
Find the total distance across all legs, and the total time across all legs. Then divide — once.
A two-part road trip
The question
A driver goes 120 km in 1.5 hours, then 80 km in 1 hour. What is the average speed for the whole trip?
120 + 80 = 200 km
1.5 + 1 = 2.5 h
200 ÷ 2.5 = 80 km/h
Cracking any word problem
1 · Underline the numbers
Find the two values you're given and note their units (240 km, 3 hours).
2 · Spot what's asked
How fast, how far or how long? That's the letter you're solving for.
3 · Check the units match
Convert minutes to hours, or km to m, before you calculate.
4 · Triangle → substitute → units
Cover the letter, put the numbers in, and write the unit on your answer.
The four classic slip-ups
⏱️ Mixing units
Using 30 minutes as "30" instead of 0.5 hours. Convert time to match your speed units first.
➗ Dividing the wrong way
Writing t ÷ d instead of d ÷ t. Trust the triangle — cover the letter you want.
🏷️ Forgetting units
An answer of "80" isn't finished. Is it km/h? m/s? Units earn marks.
📉 Rounding too early
Round only on the final line. Rounding mid-way pushes your answer off.
Speed camera check 🚨
The question
A camera records a car covering 100 m in 4 seconds. The zone limit is 60 km/h. Is the driver speeding?
100 ÷ 4 = 25 m/s
25 × 3.6 = 90 km/h
90 > 60 → speeding by 30 km/h
Practice — cover the answers!
How did you go? ✅
Everything on one page
Find speed
distance ÷ time
Find distance
speed × time
Find time
distance ÷ speed
Before you leave 🎟️
Quick check 1
A skateboarder rolls 50 m in 10 s. What is their speed in m/s?
Quick check 2
Convert 108 km/h to m/s. (Hint: ÷ 3.6)
Quick check 3
Which formula finds distance? Write it from memory.
How fast?
How far?
How long?
One formula, one triangle, one magic number (3.6). That's all it takes to answer every speed question that comes your way.