Speed, Distance and Time Formula

What is the formula for speed?

The formula for speed is speed = distance ÷ time. Speed is how much distance an object covers per unit of time, so its units are always a distance over a time, such as miles per hour (mph), kilometers per hour (km/h) or meters per second (m/s).

A car that travels 150 miles in 2.5 hours has an average speed of 150 ÷ 2.5 = 60 mph. A runner who covers 400 meters in 50 seconds averages 400 ÷ 50 = 8 m/s. The speed calculator solves for any one of the three values and shows the answer in several units at once.

Physics textbooks often write the formula as v = d ÷ t, using v for speed. Strictly, v stands for velocity, which also has a direction, while speed is just a size. If you drive to a store and back, your average velocity for the round trip is zero because you ended where you started, but your average speed is not.

How do you rearrange the speed, distance and time formula?

Multiply both sides by time to get distance = speed × time, then divide by speed to get time = distance ÷ speed. These are the same relationship, so you only need to remember one and rearrange it.

A simple memory aid is a triangle with distance on top and speed and time side by side below it. Cover the value you want, and what remains shows the calculation: distance on top of a value means divide, and two values side by side means multiply.

How do you handle hours and minutes in the formula?

Convert the time to a single unit before you calculate, usually decimal hours. Divide the minutes by 60 and add the result to the hours, so 2 hours 30 minutes is 2 + 30 ÷ 60 = 2.5 hours. Then 65 mph × 2.5 hours = 162.5 miles.

The common mistake is typing 2.30 for 2 hours 30 minutes. That means 2.3 hours, which is 2 hours 18 minutes, and it would give 149.5 miles instead of 162.5.

The same applies in reverse. When a time calculation returns a decimal, the part after the decimal point is a fraction of an hour. A 210-mile drive at 60 mph takes 3.5 hours, and 0.5 × 60 = 30 minutes, so the answer is 3 hours 30 minutes, not 3 hours 50 minutes. The speed calculator takes hours, minutes and seconds in separate boxes, which avoids the problem.

Keep the distance and speed units matched too. Miles go with mph, and kilometers go with km/h. If they differ, convert one first, using the table below.

How do you convert between mph, km/h and m/s?

Multiply mph by 1.609344 to get km/h, or by 0.44704 to get m/s. Both factors are exact, because the international mile is defined as exactly 1,609.344 meters. To go from m/s to km/h, multiply by 3.6, since an hour has 3,600 seconds and a kilometer has 1,000 meters.

The table shows values from the speed converter on our speed calculator page, rounded to two decimal places. For a quick estimate, multiply mph by 1.6 to get km/h, and halve mph to get a rough figure in m/s.

What is the average speed formula?

Average speed = total distance ÷ total time. Add up every distance in the trip, add up every time, including stops if you want your door-to-door figure, and divide.

Average speed differs from instantaneous speed, which is what your speedometer shows at a given moment. A car can spend a trip moving between 0 and 70 mph and still have one average speed for the whole journey.

Stops count if they are part of the time you measure. Driving 120 miles in 3 hours averages 40 mph, but adding a 30-minute stop makes the total 3.5 hours, and the average falls to about 34.3 mph.

Why isn't average speed the average of two speeds?

Average speed is not the average of two speeds because you spend more time at the slower speed, so the slower speed counts for more. A simple average would only work if you spent equal time at each speed.

Worked example: you drive 60 miles at 30 mph, then 60 miles back at 60 mph. Adding the speeds and halving them gives 45 mph, which is wrong. Work through it leg by leg instead.

Is there a shortcut for two legs of equal distance?

Yes. When two legs cover the same distance, average speed = 2ab ÷ (a + b), where a and b are the two speeds. This is called the harmonic mean. For 30 mph and 60 mph, 2 × 30 × 60 ÷ (30 + 60) = 3,600 ÷ 90 = 40 mph, which matches the table above.

When the two legs last the same time, the simple average does work. An hour at 30 mph plus an hour at 60 mph covers 90 miles in 2 hours, which averages 45 mph. The difference comes down to which quantity is equal: time gives the simple average, and distance gives the harmonic mean. If neither is equal, go back to total distance ÷ total time.

This also explains why a slow first half is hard to make up. If you drive 60 miles at 30 mph, you have used 2 hours. To average 60 mph over 120 miles, you would need to finish in 2 hours total, which leaves no time at all for the second leg.

Which calculator should you use for distance?

To get a distance from a speed and a time, use the speed calculator with Solve for set to distance. That is the tool for the formula in this guide.

Our distance calculator answers a different question: how far apart two points are. It works from coordinates in 2D or 3D, or from latitude and longitude, and it does not use speed or time. It is useful here only when you need a distance to feed into the formula. For example, downtown Chicago (41.8781, −87.6298) to downtown St. Louis (38.627, −90.1994) comes out at 262.2 miles in a straight line over the Earth's surface. Roads and flight paths are longer, so treat that number as a lower limit. The math behind it is covered in the distance formula guide.

For fuel on a trip of known length, the gas mileage guide uses the same kind of rearrangement: gallons = distance ÷ miles per gallon.