Enter the two values you know out of speed, distance and time. The third is calculated, along with the speed converted to m/min and m/s.
Enter speed in km/h and distance in km. For time, you can fill in just some of hours, minutes and seconds (for example, for 90 minutes enter 90 in "minutes"). Leave the value you want to find blank.
Result
Enter the two values you know out of speed, distance and time in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formula
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter any two of speed, distance and time, and the third is calculated on the spot
- Time can be entered as hours, minutes and seconds (entering just "90 minutes" or just "20 seconds" is fine too)
- Along with the speed in mph, the result also shows it converted to feet per minute (ft/min) and feet per second (ft/s). Switch "Units" to Metric to work in km/h, m/min and m/s instead
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
By default, this page calculates with speed in mph and distance in miles. To use km/h and km, switch "Units" above the calculator to Metric. For other units such as "264 feet per minute", use the converted values shown in the result.
What is this calculation used for?
Estimating travel time for a road trip
If your destination is 195 miles away and you average 65 mph on the interstate, the trip takes \(195 \div 65 = 3\) hours.
Add time for breaks and traffic, and you can decide when to leave. The estimated time of arrival on your GPS or map app is built the same way, adding up the time for each stretch of road from its expected speed.
Managing your running pace (sports)
To finish a marathon (26.2 miles) in 3 hours 30 minutes, you need an average speed of \(26.2 \div 3.5 \approx 7.49\) mph (about 7.5 mph).
Runners turn this into a pace, "minutes per mile" (about 8:01 per mile here, or about 4:59 per km), and manage their effort by checking the watch. The speed formula is the foundation of every training plan.
Understanding the average speed of trains (transportation)
Suppose a high-speed train covers 300 miles in 2 hours 30 minutes. Its average speed is \(300 \div 2.5 = 120\) mph.
That is well below its top speed of, say, 180 mph, because the time includes accelerating, slowing down and stopping at stations. Railway planners work with this stop-inclusive average speed when they build timetables.
Estimating when a storm will arrive (safety)
When the forecast says "the hurricane is moving north at 12 mph" and it is 180 miles away, you can estimate that it will take \(180 \div 12 = 15\) hours to reach you (real storms change speed and direction, so this is only a rough guide).
"Should I prepare tonight, or is tomorrow morning soon enough?" The speed formula gives you a way to think about the timing of your own safety decisions.
Getting a feel for "a 10-minute walk" (housing and everyday life)
Listings often say "a 10-minute walk to the station". A typical walking speed is about 3 mph, which is 264 feet per minute, so 10 minutes is \(264 \times 10 = 2{,}640\) feet, exactly half a mile.
Waiting at crossings and walking uphill are not included, so it may take a bit longer in real life. Knowing the speed formula, you can take the distance on a map and re-estimate the walking time for yourself.
Formula
Formula for speed
Standard notation
(the usual math form)
\(v\)
\(=\)
\(d\)
\(\div\)
\(t\)
In words
(symbols replaced with words)
③
\(v\): speed
\(=\)
①
\(d\): distance
\(\div\)
②
\(t\): time
The formula in words
①
Take the
\(d\): distance
②
divide it by the
\(t\): time
③
and you get the
\(v\): speed
Quick example
The speed of a car that covers 130 miles in 2 hours is
\(v\): speed
\(=\)
distance (130 miles)
\(\div\)
time (2 hours)
\(130 \div 2 = 65\)
Key idea
Speed is the distance covered per unit of time (per hour, per minute, per second, and so on). "130 miles in 2 hours" becomes "65 miles per 1 hour". This "per 1" division is what the speed formula really is.
The unit of the answer is "distance unit per time unit". Divide miles by hours and you get miles per hour (mph); divide feet by seconds and you get feet per second (ft/s).
Formula for distance
Standard notation
(the usual math form)
\(d\)
\(=\)
\(v\)
\(\times\)
\(t\)
In words
(symbols replaced with words)
③
\(d\): distance
\(=\)
①
\(v\): speed
\(\times\)
②
\(t\): time
The formula in words
①
Take the
\(v\): speed
②
multiply it by the
\(t\): time
③
and you get the
\(d\): distance
Quick example
The distance a car covers in 3 hours at 50 mph is
\(d\): distance
\(=\)
speed (50 mph)
\(\times\)
time (3 hours)
\(50 \times 3 = 150\)
Key idea
"50 miles per hour" × 3 hours = 150 miles. Once you see speed as an amount per 1 hour, it is natural that this is a multiplication.
The key is to match the units before multiplying. A speed in mph must be multiplied by hours, not by minutes (30 minutes has to become 0.5 hours first).
Formula for time
Standard notation
(the usual math form)
\(t\)
\(=\)
\(d\)
\(\div\)
\(v\)
In words
(symbols replaced with words)
③
\(t\): time
\(=\)
①
\(d\): distance
\(\div\)
②
\(v\): speed
The formula in words
①
Take the
\(d\): distance
②
divide it by the
\(v\): speed
③
and you get the
\(t\): time
Quick example
The time it takes to cover 150 miles at 60 mph is
\(t\): time
\(=\)
distance (150 miles)
\(\div\)
speed (60 mph)
\(150 \div 60 = 2.5\)
Key idea
This division asks: "If you go 60 miles every hour, how many hours do 150 miles take?"
If the answer is a decimal, multiply the part after the decimal point by 60 to turn it into minutes. Here the answer is 2.5 hours: 0.5 × 60 = 30, so it is 2 hours 30 minutes.
Formula to convert mph to ft/s (mph, ft/min and ft/s)
Standard notation
(the usual math form)
\(v_{\mathrm{ft/s}}\)
\(=\)
\(v_{\mathrm{mph}}\)
\(\times\)
\(5280\)
\(\div\)
\(3600\)
In words
(symbols replaced with words)
④
\(v_{\mathrm{ft/s}}\): speed in ft/s
\(=\)
①
\(v_{\mathrm{mph}}\): speed in mph
\(\times\)
②
1 mile = 5,280 ft
\(\div\)
③
1 hour = 3,600 s
The formula in words
①
Take the
\(v_{\mathrm{mph}}\): speed in mph
②
multiply it by 5280 from
1 mile = 5,280 ft
to turn the distance into feet
③
divide it by 3600 from
1 hour = 3,600 s
to turn the time into seconds
④
and you get the
\(v_{\mathrm{ft/s}}\): speed in ft/s
Quick example
30 mph converted to ft/s is
\(v_{\mathrm{ft/s}}\): speed in ft/s
\(=\)
speed (30 mph)
\(\times\)
5280
\(\div\)
3600
\(30 \times 5280 \div 3600 = 44\)
Key idea
Converting a speed is just converting the distance unit and the time unit separately. 30 mph = "158,400 ft in 1 hour" = "158,400 ft in 3,600 seconds" = "44 ft in 1 second" = 44 ft/s.
To get feet per minute instead, use "1 hour = 60 minutes" for the time: mph × 5280 ÷ 60 = ft/min (30 mph is 2,640 ft/min). To go the other way, from ft/s to mph, multiply by 3600 and divide by 5280 (44 ft/s → 30 mph). A handy fact to remember: 60 mph is exactly 88 ft/s.
Every speed calculation starts from "speed = distance ÷ time". Rearrange this one formula and you also get "distance = speed × time" and "time = distance ÷ speed". Before calculating, always check that the distance and time units match the speed unit (for mph, that is miles and hours).
Symbols and terms
Symbols
| \(v\) | vee | The symbol for speed, from the first letter of "velocity". (Example - at 50 mph, \(v = 50\)) |
| \(d\) | dee | The symbol for distance, from the first letter of "distance". (Example - for 150 miles, \(d = 150\)) |
| \(t\) | tee | The symbol for time, from the first letter of "time". (Example - for 3 hours, \(t = 3\)) |
| \(\mathrm{mph}\) | miles per hour | A unit of speed - how many miles are covered in 1 hour. "40 miles per hour" and "40 mph" are the same thing. It is the unit on US speed limit signs and car speedometers. (1 mph is about 1.61 km/h.) |
| \(\mathrm{ft/s}\) | feet per second | A unit of speed - how many feet are covered in 1 second. The slash (/) stands for "per". In science and physics, meters per second (m/s) is the standard unit instead. |
Terms
| speed | The distance covered per unit of time (per hour, per minute, per second, and so on). It is the classic example of a unit rate in elementary and middle school math. |
| distance | How far you actually travel. Strictly speaking, the straight-line distance between two points and the distance along the road can differ; the speed formula uses the distance actually traveled. |
| mph (miles per hour) | Speed written as the distance covered per 1 hour. The same speed gives different numbers in different units (30 mph = 2,640 ft/min = 44 ft/s). |
| ft/min (feet per minute) | Speed written as the distance covered per 1 minute. The same speed gives different numbers in different units (30 mph = 2,640 ft/min = 44 ft/s). |
| ft/s (feet per second) | Speed written as the distance covered per 1 second. The same speed gives different numbers in different units (30 mph = 2,640 ft/min = 44 ft/s). |
| unit rate | A way of comparing amounts by "how much per 1". Besides speed, population density (people per square mile) and fuel economy (miles per gallon) are unit rates too. |
| speed-distance-time triangle | A memory aid for the speed, distance and time formulas. Write distance at the top of a triangle and speed and time side by side at the bottom; cover the one you want and the remaining two show you the formula. Handy, but it is better to understand "speed = distance per 1 unit of time" than to rely on the picture alone. |
| average speed | The speed found from "total distance ÷ total time", which evens out the changes in speed along the way. Real vehicles keep accelerating, slowing down and stopping, so the speed you calculate is normally an average speed. |
| pace | Time per unit of distance, such as minutes per mile or minutes per km, used by runners and walkers. It is the flip side of speed - 6 mph is a pace of 10 minutes per mile (60 ÷ 6 = 10). |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Speed and unit rates (Grades 5–6) |
|
| How division and multiplication are related (Grades 3–4) |
|
| Converting units of length and time (Grades 4–5) |
|
| Working with decimals (Grades 5–6) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the speed
| Distance d (mi) | 130 |
| Time t (hours) | 2 |
| Speed v (mph) | =B1/B2 |
Table to find the distance
| Speed v (mph) | 50 |
| Time t (hours) | 3 |
| Distance d (mi) | =B1*B2 |
Table to find the time
| Distance d (mi) | 150 |
| Speed v (mph) | 60 |
| Time t (hours) | =B1/B2 |
Table to convert mph to ft/min and ft/s
| Speed (mph) | 30 |
| Converted to ft/min | =B1*5280/60 |
| Converted to ft/s | =B1*5280/3600 |
After pasting, the upper cells are your inputs and the cells starting with "=" are calculated automatically.
In the first table, for example, enter the distance 130 in B1 and the time 2 in B2, and B3 shows the speed 65 (mph). "/" is division and "*" is multiplication.
The fourth table is the unit conversion. Enter 30 mph in B1 and you get 2,640 ft/min and 44 ft/s at the same time.
In the first table, for example, enter the distance 130 in B1 and the time 2 in B2, and B3 shows the speed 65 (mph). "/" is division and "*" is multiplication.
The fourth table is the unit conversion. Enter 30 mph in B1 and you get 2,640 ft/min and 44 ft/s at the same time.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the speed
| Distance d (mi) | 130 |
| Time t (hours) | 2 |
| Speed v (mph) | =B1/B2 |
Table to find the distance
| Speed v (mph) | 50 |
| Time t (hours) | 3 |
| Distance d (mi) | =B1*B2 |
Table to find the time
| Distance d (mi) | 150 |
| Speed v (mph) | 60 |
| Time t (hours) | =B1/B2 |
Table to convert mph to ft/min and ft/s
| Speed (mph) | 30 |
| Converted to ft/min | =B1*5280/60 |
| Converted to ft/s | =B1*5280/3600 |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own.
How to calculate it in Python
distance_mi = 150 # distance (miles)
speed_mph = 60 # speed (mph)
time_hours = distance_mi / speed_mph # time taken (hours)
speed_ft_per_min = speed_mph * 5280 / 60 # converted to ft/min
speed_ft_per_sec = speed_mph * 5280 / 3600 # converted to ft/s
hours = int(time_hours) # whole-number part = hours
minutes = round((time_hours - hours) * 60) # decimal part x 60 = minutes
print(f"Time taken: {time_hours} hours ({hours} h {minutes} min)")
print(f"Speed converted: {speed_ft_per_min} ft/min / {speed_ft_per_sec} ft/s")
Runs with the standard library only. "/" is division and "*" is multiplication. This example finds the time from distance and speed, but if you change the first two variables to "speed and time" or "distance and time", the remaining value is found the same way.
How to write it in LaTeX and other math languages (copy and paste)
Formula for speed
v = d ÷ t
v = \dfrac{d}{t}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>v</mi>
<mo>=</mo>
<mfrac><mi>d</mi><mi>t</mi></mfrac>
</mrow>
</math>
v = d / t
d / t
v := d / t;
v = d / t;
v = d / t
Formula for distance
d = v × t
d = v t
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>d</mi>
<mo>=</mo>
<mi>v</mi>
<mo>⁢</mo>
<mi>t</mi>
</mrow>
</math>
d = v * t
v * t
d := v * t;
d = v * t;
d = v t
Formula for time
t = d ÷ v
t = \dfrac{d}{v}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>t</mi>
<mo>=</mo>
<mfrac><mi>d</mi><mi>v</mi></mfrac>
</mrow>
</math>
t = d / v
d / v
t := d / v;
t = d / v;
t = d / v
Formula to convert mph to ft/s (mph, ft/min and ft/s)
v[ft/s] = v[mph] × 5280 ÷ 3600
v_{\mathrm{ft/s}} = v_{\mathrm{mph}} \times \dfrac{5280}{3600}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>v</mi><mtext>ft/s</mtext></msub>
<mo>=</mo>
<msub><mi>v</mi><mtext>mph</mtext></msub>
<mo>×</mo>
<mfrac><mn>5280</mn><mn>3600</mn></mfrac>
</mrow>
</math>
v_(ft/s) = v_(mph) * 5280 / 3600
v * 5280 / 3600
v_fts := v_mph * 5280 / 3600;
v_fts = v_mph * 5280 / 3600;
v_(ft/s) = v_(mph) × 5280 / 3600
How to have ChatGPT do the calculation
You are a calculation assistant for speed, distance and time. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). A car travels 150 miles at 60 mph. Find each of the following: 1. The time taken (also show it in the form "X hours Y minutes") 2. This speed converted to feet per minute (ft/min) 3. This speed converted to feet per second (ft/s) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Related Features
Average Calculator (Mean)
Enter your numbers to get the average, the sum and more at once. The same idea is behind "average speed"
Percentage Calculator (Percent, Part and Whole)
Enter any two of the base amount, the part and the percentage, and get the third. Like speed, it finds one value from the other two
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