Formula for Speed
A runner covers 100 meters in 12.5 seconds – how fast are they going? A truck drives 480 km in 6 hours – what is its average speed? Both questions come down to one relationship: the formula for speed. Below you will find the core equation, its rearrangements, unit conversions, worked examples, and an online calculator that solves it instantly.
Average Speed Calculator
For trips with multiple segments, average speed = total distance ÷ total time – not the simple average of individual speeds.
What Is the Formula for Speed?
The basic formula for speed is:
v = d / t
| Symbol | Meaning | SI Unit |
|---|---|---|
| v | Speed | m/s |
| d | Distance | m |
| t | Time | s |
Speed tells you how much distance an object covers per unit of time. If a car travels 300 kilometers in 5 hours, its speed is 300 / 5 = 60 km/h.
Rearranged Forms
The same relationship gives you distance or time when the other two values are known:
- Distance: d = v × t
- Time: t = d / v
These three forms cover most everyday and exam-style physics problems.
Common Units and Conversions
Different contexts use different units. Here are the most frequent ones and how they relate:
| From | To | Multiply by |
|---|---|---|
| m/s | km/h | 3.6 |
| km/h | m/s | 0.2778 |
| mph | km/h | 1.6093 |
| km/h | mph | 0.6214 |
| knots | km/h | 1.852 |
A person walking at 1.4 m/s is moving at 1.4 × 3.6 = 5.04 km/h. A highway speed limit of 65 mph equals 65 × 1.6093 ≈ 104.6 km/h.
Average Speed vs Instantaneous Speed
Average Speed
Average speed is total distance divided by total time, regardless of how speed varied along the way:
v_avg = d_total / t_total
Example: You drive 180 km in the first 2 hours, then stop for 30 minutes, then drive another 90 km in 1.5 hours.
- Total distance = 180 + 90 = 270 km
- Total time = 2 + 0.5 + 1.5 = 4 h
- Average speed = 270 / 4 = 67.5 km/h
The stop time counts – average speed drops because no distance was covered during that half hour.
Instantaneous Speed
Instantaneous speed is the speed at a single moment. A car’s speedometer reads instantaneous speed. Mathematically, it is the derivative of distance with respect to time: v = dd/dt. For constant speed, instantaneous speed equals average speed.
How Does Speed Differ from Velocity?
| Property | Speed | Velocity |
|---|---|---|
| Type | Scalar | Vector |
| Includes direction | No | Yes |
| Can be negative | No | Yes |
| Example | 80 km/h | 80 km/h east |
In one-dimensional motion along a straight line, velocity carries a sign (positive or negative) to indicate direction. Speed is the absolute value of velocity: speed = |velocity|.
Step-by-Step Examples
Example 1 – Finding Speed
A cyclist rides 45 km in 1.5 hours. What is the speed?
- Identify values: d = 45 km, t = 1.5 h
- Apply formula: v = d / t = 45 / 1.5
- Result: 30 km/h
Example 2 – Finding Distance
A train moves at 120 km/h for 2.25 hours. How far does it travel?
- Identify values: v = 120 km/h, t = 2.25 h
- Apply formula: d = v × t = 120 × 2.25
- Result: 270 km
Example 3 – Finding Time
A plane must cover 3,200 km at a cruising speed of 800 km/h. How long will the flight take?
- Identify values: d = 3,200 km, v = 800 km/h
- Apply formula: t = d / v = 3,200 / 800
- Result: 4 hours
Example 4 – Two-Segment Average Speed
You walk 4 km at 5 km/h, then run 6 km at 12 km/h. What is your average speed?
- Time for first segment: t₁ = 4 / 5 = 0.8 h
- Time for second segment: t₂ = 6 / 12 = 0.5 h
- Total distance: d = 4 + 6 = 10 km
- Total time: t = 0.8 + 0.5 = 1.3 h
- Average speed: v = 10 / 1.3 ≈ 7.69 km/h
Notice that average speed is not the simple mean of 5 and 12. You must always divide total distance by total time.
Related Formulas in Kinematics
Speed is the foundation for several other motion equations:
| Formula | Meaning |
|---|---|
| a = (v − u) / t | Acceleration (change in speed over time) |
| v = u + at | Final speed under constant acceleration |
| v² = u² + 2ad | Speed from acceleration and displacement |
| d = ut + ½at² | Displacement under constant acceleration |
In these formulas, u is initial speed, v is final speed, a is acceleration, and t is time.
Speed of Common Objects (Reference)
| Object / Situation | Typical Speed |
|---|---|
| Walking | 4–5 km/h |
| Cycling (casual) | 15–25 km/h |
| City traffic | 30–50 km/h |
| Highway driving | 90–130 km/h |
| Commercial jet | 800–950 km/h |
| Speed of sound (air, 20 °C) | 1,236 km/h |
| Speed of light (vacuum) | 1,079,252,849 km/h |
The speed values above are approximate and depend on conditions such as terrain, traffic, or atmospheric properties.
How to Use the Calculator Above
The calculator at the top of this page solves the speed formula in any direction:
- To find speed – enter distance and time
- To find distance – enter speed and time
- To find time – enter speed and distance
Select your preferred units (meters, kilometers, miles, seconds, hours), and the calculator converts the result automatically. It applies the same v = d / t relationship described throughout this article, so you can verify any manual calculation in seconds.
This article provides general physics formulas for educational purposes. For applications in engineering, navigation, or safety-critical systems, always verify calculations against domain-specific standards and regulations.