Convert mph to m/s miles per hour ↔ metres per second Free Online Secure
Type a value in miles per hour and read it in metres per second at once. The factor is exact by definition, the arithmetic happens in your browser, and nothing is sent anywhere.
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Convert from miles per hour
Convert to metres per second
Common values — Convert mph to m/s (miles per hour ↔ metres per second)
| mph | m/s |
|---|---|
| 1 | 0.44704 |
| 2 | 0.89408 |
| 3 | 1.34112 |
| 5 | 2.2352 |
| 10 | 4.4704 |
| 20 | 8.9408 |
| 50 | 22.352 |
| 100 | 44.704 |
Where these units come from
Speed has no unit of its own: it is a length divided by a time, so every trade simply kept the length it was already using. That is why the same motion is 100 km/h on a European road sign, 62 mph on an American one and 27.8 m/s in a physics problem. The knot is the oldest of them and the most literal: sailors paid out a line with knots tied at even spacing and counted how many ran through their fingers while a sand glass emptied, so the speed was read off in knots. One knot is one nautical mile per hour, and a nautical mile is a minute of latitude — which is why ships and aircraft still use it. The speed of light is the odd one out: since 1983 it is not measured but fixed at exactly 299,792,458 m/s, because the metre is now defined from it.
Where you meet them
Kilometres and miles per hour live on speedometers and road signs, metres per second in physics, engineering and wind reports, feet per second in ballistics and in American machine shops. Knots carry shipping, aviation and marine weather, and Mach numbers appear wherever an aircraft is fast enough for the air's own stiffness to matter. The speed of light turns up less in daily life than in distances: a light year is simply how far it gets in one.
Questions people ask
Is Mach 1 a fixed speed?
No. Mach is a ratio to the speed of sound in the surrounding air, and sound travels more slowly in colder air. This page uses the standard sea-level figure, 340.294 m/s, so Mach 1 here is about 1225 km/h. At the altitude airliners cruise at, the air is some 50 degrees colder and the same Mach 1 is roughly a tenth slower. An aircraft can therefore hold a constant Mach number while its speed over the ground changes.
Why do ships and aircraft use knots rather than km/h?
Because a nautical mile is one minute of arc of latitude. A vessel making one knot covers one minute of latitude in an hour, so speed, time and position on a chart fit together without conversion. The same reasoning kept the nautical mile at exactly 1852 metres rather than rounding it to something tidier.
Is the answer exact?
Where both units are defined in terms of one another by whole numbers, yes — the page says so above the figure, and the only rounding is in how many digits are shown. Where the ratio has no finite decimal, the page shows twelve significant digits and says the relation is approximate rather than pretending otherwise.
Does anything I type leave my device?
No. The arithmetic runs in your browser; nothing is uploaded and there is no server to upload it to. Load the page once and it keeps working with the network switched off.
The physics of the fastball: from mph to m/s
The radar gun says 98 miles per hour. A physics student wants to know how much kinetic energy the ball carries, how long it takes to reach the plate and how far it would fly if nothing stopped it. Every one of those answers needs speed in metres per second. American sports broadcasts tell the story in mph, and the equations of motion want SI units. To convert mph to m/s, multiply by 0.447: 60 mph is 26.8 m/s, 100 mph is 44.7 m/s and 130 mph is 58.1 m/s. The calculator above multiplies as you type, and the sections below turn well-known sports speeds into physics.
You will find the rule with worked examples, a short profile of each unit, a comparison, a long set of solved sports problems and the slips to avoid. The arithmetic runs in your browser, and what you type is not sent anywhere.
How to convert mph to m/s: multiply by 0.447
The rule
One mile is 1,609.344 metres and one hour is 3,600 seconds, so one mile per hour is 0.44704 m/s. To convert mph to m/s, multiply the mph figure by 0.447. So 30 mph is 13.4 m/s, 75 mph is 33.5 m/s and 200 mph is 89.4 m/s. To go back, multiply by 2.237.
Worked examples
A 95 mph fastball is 42.5 m/s. A 120 mph tennis serve is 53.6 m/s. A 170 mph golf ball is 76 m/s, and a 100 mph slap shot is 44.7 m/s.
Why 0.447
The factor is exact for today's definitions: 1,609.344 metres divided by 3,600 seconds. For a quick estimate, take half the number and subtract a tenth of that half.
A quick sanity test
The m/s figure is a little under half the mph figure. If a “convert mph to m/s” calculation result is bigger than the starting number, you used 2.237 instead.
The mile per hour
The unit of American sports
The mile per hour is the unit on the scoreboard graphics of baseball, tennis, golf, hockey and football in the United States. Fans know that 100 is a landmark for a pitcher, 130 for a tennis serve, and 70 for a driver's swing.
Where it appears
Broadcast graphics, scouting reports and coaching notes.
The metre per second
The unit of the equations
The metre per second is the SI unit of speed. Newtons, joules and watts are defined from it, so a physics problem that asks for energy, momentum or range expects the speed in m/s.
Where it appears
Physics lessons, biomechanics papers and engineering calculations.
Miles per hour against metres per second
One mph is 0.447 m/s, so a figure in m/s is a little under half the figure in mph. A 100 mph pitch is 44.7 m/s. The two numbers describe the same ball, but only the second fits into the formula for kinetic energy, half the mass times the speed squared. Using 100 directly would overstate the energy by a factor of five, which a “convert mph to m/s” calculation avoids.
The factor is exact, so no rounding enters. The only trap is direction: from mph to m/s the number falls.
Where the conversion shows up
Problem 1: time to the plate
A pitcher releases the ball about 55 feet, or 16.8 m, from the plate at 95 mph. The speed is 42.5 m/s, so the ball covers that distance in about 0.40 seconds, ignoring drag. With drag the ball loses about 8 per cent of its speed on the way, so the real time is nearer 0.43 seconds. A “convert mph to m/s” calculation starts every such estimate.
Problem 2: kinetic energy
A baseball has a mass of 0.145 kg. At 95 mph, which is 42.5 m/s, its kinetic energy is half times 0.145 times 42.5 squared, or 131 joules. At 100 mph, 44.7 m/s, it is 145 joules. A 5 mph increase adds 10 per cent. Using mph in the formula would give 654, a figure with no meaning.
Problem 3: a tennis serve
A serve of 120 mph, which is 53.6 m/s, travels the 18.4 metres from the baseline to the far service line area in about 0.35 seconds before slowing. A tennis ball of 58 g carries 83 joules at that speed. Returners have well under half a second, which is why anticipation matters more than reflexes.
Problem 4: the golf drive
A professional's ball speed is about 170 mph, or 76 m/s. A golf ball of 45.9 g carries 133 joules. Clubhead speed is around 115 mph, which is 51.4 m/s. The ratio of ball speed to club speed, the smash factor, is 1.48. A “convert mph to m/s” calculation on both speeds gives the figure, and a launch monitor displays it in mph.
Problem 5: the Magnus effect
A spinning ball curves because of the Magnus force. For a pitch at 90 mph, or 40.2 m/s, with 2,400 rpm of spin, the ball deviates by roughly 40 cm over the distance to the plate relative to a spinless path. Sports scientists compute the spin and speed in SI units, so the pitch in mph is the first thing converted.
Problem 6: momentum and impact
The momentum of a 0.145 kg ball at 42.5 m/s is 6.2 kg·m/s. If it is stopped by a catcher's mitt in 10 milliseconds, the average force is 620 newtons, the weight of about 63 kg. The mitt is padded to spread the force over a longer time. Equipment designers make such calculations in SI units, starting from the speed in mph given by the league.
Problem 7: relative speed
A runner at 20 mph, which is 8.9 m/s, chasing a ball thrown at 30 mph, or 13.4 m/s, in the same direction has a closing speed of 4.5 m/s if the throw is along the runner's path. If the ball goes the other way, the relative speed is 22.3 m/s. These calculations appear in basic mechanics courses, with speeds supplied in mph from sports.
Problem 8: skiing and sledding
A downhill skier at 80 mph is moving at 35.8 m/s. A bobsled at 90 mph is at 40.2 m/s. The kinetic energy of a 100 kg skier with equipment at 35.8 m/s is 64 kilojoules, equal to a fall from 65 metres. Course designers set safety nets and slopes using the speed in SI units.
Problem 9: running with a dog
A person jogging at 6 mph, or 2.7 m/s, with a dog that sprints at 25 mph, or 11.2 m/s, in bursts, finds the dog gaining 8.5 m/s on the person. A dog can maintain 15 mph, or 6.7 m/s, for some minutes. Problems of this kind are good practice for relative-speed exercises that begin with mph.
Spreadsheet formulas
Place speeds in mph in column A and use =A2*0.44704 in column B. For kinetic energy, use =0.5*mass*B2^2. For the reverse, use =B2*2.23694. Label each column with its unit and use one decimal for speeds.
Rounding and precision
The factor is exact: 100 mph is 44.704 m/s. Radar guns read to the nearest mph, so 44.7 is enough, and a result like 131.2 joules should be given as about 130. Keep a few extra digits in the working, because the speed is squared in the energy formula.
A mental shortcut
Halve the mph and take away a tenth of the half. For 100 mph: 50 minus 5 gives 45 m/s, close to the exact 44.7. For 60 mph: 30 minus 3 gives 27, against 26.8. The error is about half a per cent.
Landmarks to memorise
10 mph is 4.5 m/s, 25 mph is 11.2 m/s, 60 mph is 26.8 m/s, 90 mph is 40.2 m/s, 100 mph is 44.7 m/s and 130 mph is 58.1 m/s. These landmarks help you turn a broadcast number into a physics quantity.
Reference ladder
5 mph is 2.2 m/s. 15 mph is 6.7 m/s. 35 mph is 15.6 m/s. 55 mph is 24.6 m/s. 80 mph is 35.8 m/s. 120 mph is 53.6 m/s. 150 mph is 67.1 m/s. 200 mph is 89.4 m/s. A ladder like this speeds up a quick check.
Problem 10: the hockey slap shot
A puck of 170 g at 100 mph, which is 44.7 m/s, has a kinetic energy of 170 joules. From 15 metres away it takes 0.34 seconds to reach the goal. The fastest recorded shot is about 108.8 mph, which is 48.6 m/s. The goalie sees the puck for a third of a second, which is why position matters more than reaction.
Checking by reversing
To check any convert mph to m/s result, multiply it by 2.237. If 100 mph became 44.7 m/s, then 44.7 times 2.237 is 100. A second test is the size: the m/s figure is a little under half of the mph figure.
Relation to km/h
One mph is 1.609 km/h, and one m/s is 3.6 km/h. A 95 mph pitch is 152.9 km/h and 42.5 m/s. Broadcasts for international audiences show km/h, and research papers m/s. Knowing both conversions lets you read a news report, a scouting report and a paper without getting lost.
Safety in youth sports
Youth leagues limit pitch speed for safety. A 12-year-old pitching at 60 mph, which is 26.8 m/s, produces much less force than an adult at 90 mph, or 40.2 m/s. Helmets and face guards are tested at the speeds seen in each age group. A parent reading a safety standard in m/s can use a “convert mph to m/s” calculation to compare it with the league's mph figures.
Radar and timing
A radar gun measures the ball's speed through the Doppler shift, with a typical accuracy of 1 mph, which is 0.45 m/s. Camera systems track the ball in three dimensions and compute speed at several points. A pitch released at 95 mph and arriving at 87 mph shows a loss of 8 mph, or 3.6 m/s, caused by drag over 55 feet.
Problem 11: a thrown football and the arc
A pass thrown at 24.6 m/s at 35 degrees has a horizontal speed of 20.1 m/s and a vertical speed of 14.1 m/s. It stays in the air for 2.9 seconds and lands 58 metres away, about 63 yards, if the receiver is at the same height. Breaking a throw into components is standard physics, and a “convert mph to m/s” calculation supplies the starting speed from the broadcast figure.
Problem 12: stopping a fast ball
A 0.145 kg ball arrives at 42.5 m/s and is brought to rest by a glove that gives way 8 centimetres. The deceleration is v squared over twice the distance, which is 11,289 m/s², about 1,150 g, and the average force is 1,637 newtons. Gloves with padding double the stopping distance and halve the force. Safety standards for catcher's gear are quoted in the speeds of the league, converted from mph.
Problem 13: cricket
A fast bowler delivers at 90 mph, which is 40.2 m/s. The pitch is 20.12 metres long, so the ball reaches the batter in about 0.5 seconds, slowing a little. The record is about 100.2 mph, which is 44.8 m/s. Batters rely on watching the bowler's wrist and the ball's seam more than on speed alone.
Problem 14: a quarterback's pass
A professional quarterback throws at 55 mph, which is 24.6 m/s. A football of 0.42 kg then has 127 joules. A pass over 40 yards, or 36.6 metres, takes about 1.6 seconds including the arc. Coaches compare throwing speeds in mph, while sports scientists measure them in m/s with radar.
Problem 15: how far could it fly
In a vacuum, a ball launched at 45 degrees with speed v travels v squared over g. For 100 mph, which is 44.7 m/s, the range would be 204 metres. Air reduces this to about 120 metres for a baseball, because drag is large at this speed. The gap shows why air resistance matters, and the vacuum answer is a clean exercise in unit conversion.
Problem 16: bat and ball
A bat swing of 70 mph, or 31.3 m/s, meeting a pitch of 90 mph, or 40.2 m/s, can send a ball off at about 102 mph, which is 45.6 m/s. A rule of thumb says exit speed is about 0.2 times the pitch speed plus 1.2 times the bat speed, a quick estimate that depends on the units being consistent, so a “convert mph to m/s” calculation on both inputs comes first.
Problem 17: sprint speed
A sprinter at 27.8 mph is moving at 12.4 m/s. A football player running at 22 mph is at 9.8 m/s. Over 40 yards, or 36.6 m, at an average of 8 m/s the time is 4.6 seconds, matching a good combine time. The figures are widely quoted in mph in American media, and the biomechanical studies use m/s.
Problem 18: soccer shots
A strong shot reaches 70 mph, which is 31.3 m/s, and the record is above 130 mph, or 58 m/s. A ball of 430 g at 31.3 m/s carries 211 joules. From 20 metres away a goalkeeper has 0.64 seconds. American soccer broadcasts show mph, and the same shot elsewhere is quoted in km/h, 113.
Problem 19: volleyball and badminton
A volleyball serve at 70 mph is 31.3 m/s, and a spike can reach 80 mph, which is 35.8 m/s. A badminton smash at 300 mph is 134 m/s, the fastest of all racket sports, though the shuttlecock slows rapidly. A “convert mph to m/s” calculation puts these three on a single table for comparison.
More values for convert mph to m/s
A longer list of conversions
If the value you need is not in the first list, these further conversions may be close enough to read off directly:
- 0.1 mph = 0.044704 m/s
- 0.5 mph = 0.22352 m/s
- 3 mph = 1.34112 m/s
- 4 mph = 1.78816 m/s
- 7 mph = 3.12928 m/s
- 15 mph = 6.7056 m/s
- 20 mph = 8.9408 m/s
- 75 mph = 33.528 m/s
- 200 mph = 89.408 m/s
- 500 mph = 223.52 m/s
- 2,000 mph = 894.08 m/s
- 10,000 mph = 4,470.4 m/s
Common slips when you convert mph to m/s
Multiplying by 2.237
From mph to m/s the number falls. If 100 mph became 223.7, you used the factor for the other direction.
Putting mph into an energy formula
Energy needs m/s. Using mph gives a number that is wrong by a factor of five.
Confusing release speed with plate speed
The speed at release is higher than at the plate, because drag slows the ball. State which one you mean.
Short answers
How do I convert mph to m/s?
Multiply by 0.447.
What is 100 mph in m/s?
44.7 m/s.
What is 60 mph in m/s?
26.8 m/s.
How many mph is 1 m/s?
2.237 mph.
Does my number leave my device?
No, the calculation runs in your browser.
More pages and a wrap-up
For other speed conversions see Convert mph to km/h, Convert mph to Mach, Convert km/h to m/s, Convert c to m/s, Convert m/s to ft/s, Convert km to mi, Convert mi to km, Convert °C to °F, Convert °F to °C. The reverse direction is Convert m/s to mph.
In short, a “convert mph to m/s” calculation means multiplying by 0.447 and writing the unit beside the answer. Your number is computed locally, with no account and no upload.