The Speed Formula, Explained with Examples

Speed answers a simple question: how much ground does something cover in a given amount of time? It is one of the first formulas you meet in science, and it powers everything from running pace to driving estimates to physics homework. In this guide you will see the core formula, how to rearrange it to find distance or time, how speed differs from velocity, the units to watch, and several worked examples you can follow step by step.

What is speed?

Speed is how fast an object moves, measured as the distance it travels divided by the time it takes. Because it describes only a size and not a direction, speed is a scalar quantity. A car travelling at 60 km/h has a speed of 60 km/h whether it heads north, south, or around a roundabout. The number alone tells the whole story.

The key word in the definition is distance. Distance is the total length of the path actually travelled. If you walk 5 m east and then 5 m back west, the total distance is 10 m, even though you ended up where you started. Speed uses that full path length, which is one of the things that separates it from velocity, as you will see below.

The speed formula

The core relationship could not be simpler. Speed equals distance over time:

The standard SI unit is metres per second (m/s), but you will also see kilometres per hour (km/h), miles per hour (mph), and other distance-over-time units. As long as the top of the fraction is a length and the bottom is a duration, you have a valid speed unit. The same distance-over-time idea underlies the average rate of change you may meet in other settings, and you can measure a straight-line distance between two points with the distance calculator.

It helps to know a few common conversions so your answers land in the units a question expects. To go from metres per second to kilometres per hour, multiply by 3.6, so 5 m/s becomes 18 km/h. To convert the other way, divide by 3.6. For miles per hour, 1 m/s is roughly 2.24 mph. Here are the conversions you will reach for most often.

Rearranging the formula: distance and time

The real power of the speed formula is that you can rearrange it to solve for whichever quantity is missing. Because speed, distance, and time are tied together by a single equation, knowing any two of them lets you find the third.

A handy memory aid is the formula triangle. Picture distance on top, with speed and time sitting side by side underneath. Cover the quantity you want and the triangle shows you what to do with the other two: cover distance and you are left with speed times time; cover time and you are left with distance over speed. Here is the same idea laid out as a table.

Speed vs velocity: the key difference

People use speed and velocity interchangeably in everyday talk, but in physics they are distinct. Speed is the magnitude of velocity, which means velocity is speed plus a direction. A car going 60 km/h has a speed of 60 km/h, but its velocity is 60 km/h in a specific direction, say north. Here is a side-by-side comparison.

Because of these differences, average speed and the size of average velocity are not always equal. On a round trip back to where you started, your average speed can be high while your displacement, and therefore your average velocity, is exactly zero. To go deeper on the directional version, see the velocity formula guide, and to learn how speed changes over time, read the acceleration formula explained.

Worked example: finding speed

A runner covers 400 metres in 50 seconds along a track. Find the average speed.

1. Identify the total distance: 400 metres.
2. Identify the total time: 50 seconds.
3. Apply the formula: speed = distance / time = 400 / 50.
4. Divide: 400 divided by 50 equals 8.
5. State the answer with units: the average speed is 8 m/s.

If a question wants the result in km/h, multiply by 3.6, so 8 m/s becomes 28.8 km/h.

Worked example: finding distance

A car drives at a steady 90 km/h for 2.5 hours. How far does it travel?

1. List the values: speed = 90 km/h, time = 2.5 hours.
2. Choose the right form: distance = speed x time.
3. Multiply: 90 x 2.5 = 225.
4. Check the units: km/h times hours leaves kilometres.
5. State the answer: the car travels 225 kilometres.

Worked example: finding time

A cyclist rides 30 km at a steady 20 km/h. How long does the ride take?

1. List the values: distance = 30 km, speed = 20 km/h.
2. Choose the right form: time = distance / speed.
3. Divide: 30 / 20 = 1.5.
4. Check the units: km divided by km/h leaves hours.
5. State the answer: the ride takes 1.5 hours, or 1 hour 30 minutes.

Watch the decimal here: 1.5 hours is 1 hour and 30 minutes, not 1 hour and 50 minutes. To turn the fractional part into minutes, multiply it by 60, so 0.5 x 60 = 30 minutes.

Worked example: average speed over a trip

Someone drives 120 km in 2 hours, stops, then drives another 60 km in 1 hour. Find the average speed for the whole journey.

1. Add up the total distance: 120 + 60 = 180 km.
2. Add up the total time: 2 + 1 = 3 hours.
3. Apply average speed = total distance / total time = 180 / 3.
4. Divide: 180 divided by 3 equals 60.
5. State the answer: the average speed is 60 km/h.

Notice that average speed is not the simple average of 60 km/h and 60 km/h here by luck; in general you must add all the distance and all the time first, then divide once. Averaging the two leg speeds directly gives the wrong answer whenever the legs take different amounts of time.

Common mistakes to avoid

• Averaging two speeds directly. Average speed is total distance over total time, not the mean of the leg speeds, unless each leg takes the same time.
• Mixing units. Keep distance and time in matching units before dividing, for example metres with seconds or kilometres with hours, and convert first if they do not match.
• Confusing speed with velocity. Speed has no direction; adding a direction turns it into a velocity. See the velocity formula for the directional version.
• Forgetting to include stops. When a question asks for average speed over a journey, idle time still counts as part of the total time.
• Dropping the units in the answer. A speed of 8 means little until you say 8 m/s or 8 km/h.

Good to know

Average speed and instantaneous speed are different. Average speed covers a whole interval, while instantaneous speed is the speed at a single moment, which is what a car speedometer reads. The two are equal only when speed is constant. Speed also connects to other formulas: it is the building block of momentum and kinetic energy, both of which depend on how fast an object moves. If you need to measure how far apart two points are before applying the formula, the tool below makes it quick.

The speed formula is short, but it carries a lot of weight. Once you can confidently move between speed = distance / time, distance = speed x time, and time = distance / speed, you can solve a huge range of motion problems, from race pacing to travel planning to first-year physics. Keep your units consistent, remember that average speed uses totals, and you will rarely go wrong.