One formula, three questions
Speed tells you how much distance you cover in a unit of time. Write it as s = d / t, where d is distance and t is time. Once you have that, the other two forms fall out with basic algebra: d = s x t and t = d / s.
So any problem with two of the three values is solvable. A car covering 150 km in 2 hours goes 75 km/h. A cyclist riding 18 km/h for 2.5 hours covers 45 km. A 42 km trip at 84 km/h takes half an hour.
Formula notes
Speed: s = d / tDistance: d = s x tTime: t = d / s
The triangle trick
Many students learn this with a triangle. Put D on top, and S and T side by side underneath. Cover the value you want. If D is left over S and T, divide. If S and T sit next to each other, multiply.
Cover S and you see D over T, so speed is distance divided by time. Cover D and you see S next to T, so distance is speed times time. It's a memory aid for the same three formulas, nothing more.
Get the units right first
Most wrong answers come from units, not algebra. If speed is in km/h, time has to be in hours. If it's in m/s, time has to be in seconds. Convert before you plug numbers in.
Minutes to hours means dividing by 60, so 40 minutes is 0.667 hours. To turn km/h into m/s, divide by 3.6. For mph and km/h, use 1.609344, the exact number of kilometers in a mile.
- 40 minutes = 40 / 60 = 0.667 hours
- 90 km/h = 90 / 3.6 = 25 m/s
- 60 mph = 60 x 1.609344 = 96.56 km/h
- 10 m/s = 10 x 3.6 = 36 km/h
Worked problems
A train covers 240 km in 2 hours 40 minutes. What's its average speed? Convert the time: 2 + 40/60 = 2.667 hours. Then 240 / 2.667 = 90 km/h.
A sprinter runs 100 m in 12.5 seconds. That's 100 / 12.5 = 8 m/s, or 8 x 3.6 = 28.8 km/h. A hiker walks at 5 km/h for 3 hours 15 minutes. Distance = 5 x 3.25 = 16.25 km. You can check any of these with our speed calculator, which handles the unit conversions for you.
Flipping speed into pace
Runners and walkers often flip the formula around. Pace is time per distance, the reciprocal of speed. To get minutes per mile, divide 60 by your speed in mph. To get minutes per kilometer, divide 60 by your speed in km/h.
At 7.5 mph, pace is 60 / 7.5 = 8 minutes per mile. At 12 km/h it's 5 minutes per kilometer. A 3 mph walk is 20 minutes per mile. Faster speed means a smaller pace number, which feels backwards until you remember pace counts time.
Formula notes
Minutes per mile = 60 / speed in mphMinutes per km = 60 / speed in km/h
Mistakes to avoid
Don't average two speeds to get a trip average. If you cover equal distances at 30 and 60 mph, you spend twice as long at the slower speed, so the average is 40 mph, not 45. Work out total distance and total time instead.
Watch decimal time. 2.30 hours is 2 hours 18 minutes, not 2 hours 30. And keep speed and velocity apart in physics problems. Velocity uses displacement and direction, so a round trip that ends where it started has zero average velocity even though the speed wasn't zero.
Frequently asked questions
What is the unit of speed in physics?
The SI unit is meters per second (m/s). Everyday speeds are usually given in km/h or mph.
How do you find time when you know distance and speed?
Divide distance by speed. 150 miles at 50 mph takes 150 / 50 = 3 hours.
Is speed a vector?
No. Speed is a scalar, just a size. Velocity is the vector version, with a direction attached.
How do I convert m/s to km/h?
Multiply by 3.6. So 8 m/s is 28.8 km/h. To go from km/h to m/s, divide by 3.6.
References
These sources support the method or guidance used for Speed Calculator. Verify time-sensitive rules at the source.
Try the calculator
Open Speed Calculator, enter your scenario, and compare its supporting rows with this guide's method and checks.