Speed, distance, and time are connected by one of the most fundamental relationships in maths and physics. Whether you're planning a road trip, training for a race, answering a GCSE maths question, or estimating travel times, the same formula applies in every case. This guide breaks it all down with clear examples and useful unit conversions.
The Core Formula
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
These three equations are simply rearrangements of the same relationship. The "formula triangle" is the classic way to remember them: write S, D, T in a triangle (D on top, S and T on bottom). Cover the one you want to find — the remaining two show whether to multiply or divide.
Units: Getting Them Right
The most common errors in speed-distance-time problems involve unit mismatches. You must ensure your units are consistent before applying the formula:
| Speed unit | Distance unit | Time unit |
|---|---|---|
| mph (miles per hour) | miles | hours |
| km/h (kilometres per hour) | kilometres | hours |
| m/s (metres per second) | metres | seconds |
| min/km (pace) | kilometres | minutes |
Key conversion: If time is given in hours and minutes, convert entirely to hours first: e.g. 2 hours 30 minutes = 2.5 hours.
Worked Examples
Example 1: Finding Speed (Driving)
You drive 180 miles in 3 hours. What is your average speed?
Speed = Distance ÷ Time = 180 ÷ 3 = 60 mph
Example 2: Finding Distance (Running)
You run at 8 km/h for 45 minutes. How far do you run?
First: convert 45 minutes to hours = 45 ÷ 60 = 0.75 hours
Distance = Speed × Time = 8 × 0.75 = 6 km
Example 3: Finding Time (Train Journey)
A train travels 385 km at an average speed of 110 km/h. How long does the journey take?
Time = Distance ÷ Speed = 385 ÷ 110 = 3.5 hours = 3 hours 30 minutes
Example 4: Pace (Running Training)
You want to run a 10 km race in 55 minutes. What pace do you need?
Pace = Time ÷ Distance = 55 ÷ 10 = 5 min 30 sec per km
To convert to km/h: Speed = 60 ÷ 5.5 = 10.9 km/h
Speed Unit Conversions
| From | To | Multiply by |
|---|---|---|
| mph | km/h | 1.60934 |
| km/h | mph | 0.62137 |
| m/s | km/h | 3.6 |
| km/h | m/s | 0.27778 |
| mph | m/s | 0.44704 |
| knots | km/h | 1.852 |
Average Speed vs Instantaneous Speed
The formula gives you average speed over the entire journey — total distance divided by total time, including stops. Instantaneous speed is what a speedometer shows at any given moment.
This matters for journey planning: a 200-mile motorway drive averaging 65 mph takes 3 hours 4 minutes. But with a 20-minute fuel stop, your effective average drops to 200 ÷ (3.07 + 0.33) = 59 mph, taking 3 hours 24 minutes door-to-door.
Physics Applications
In physics, speed and velocity are related but distinct:
- Speed is scalar (magnitude only): 50 km/h
- Velocity is vector (magnitude + direction): 50 km/h due north
For GCSE Physics, the formula is the same but problems often involve displacement (vector distance) rather than distance. When an object travels in a straight line without changing direction, displacement = distance and the distinction doesn't matter practically.
Real-World Applications
- Road trip planning: Estimate journey time accounting for stops
- Running training: Calculate pace targets for races
- Cycling: Estimate completion time for sportive events
- Aviation: Flight time = distance ÷ ground speed (adjusted for wind)
- Emergency response: Calculate how quickly an ambulance can reach a patient
Summary
Speed = Distance ÷ Time. Distance = Speed × Time. Time = Distance ÷ Speed. Always ensure units are consistent — convert everything to matching units before calculating. For multi-leg journeys, calculate total distance and total time separately, then divide to get average speed. Use our speed calculator for instant results across any unit combination.