# Speed Converter

Created by Davide Borchia
Last updated: Jul 07, 2022

Speed is an everyday quantity: learn how to convert speed between various units of measurement with our converter. Here you will learn units fit for any context, from a walk to a journey to the stars!

• What is speed?
• How do we measure speed? The units of measurement of speed;
• The meter per second and the foot per second;
• The kilometer per hour and the mile per hour;
• Knots and Beaufort scale: speed conversion calculations for meteorologists and pilots;
• Ludicrous speed: to the stars!

## What is speed?

Speed is the rate at which a body changes position in time. Alternatively, you can define speed as the distance covered in a certain amount of time. Remember that speed is not the same as velocity: the first one doesn't contain any information about the direction of the motion (and hence can't assume negative values).

## Units of measurement of speed

The measurement units of speed depend directly on the ones used for length and time. To start our journey through these units, it's better to introduce the most versatile unit for the speed: the meter per second, $\text{m}/\text{s}$: this unit, deriving from two SI base units, is widely used worldwide. Its US customary system counterpart is the foot per second, where only the length has a different unit. The conversion of speed between meters per second and feet per second is:

\begin{align*} 1\ \text{m}/\text{s} = 3.281\ \text{ft}/\text{s}\\ 1\ \text{ft}/\text{s} = 0.3048\ \text{s}/\text{s} \end{align*}

These two units are the most commonly used in physics. However, for our daily lives, their multiples are slightly better suited. Let's meet them.

## Convert speed units multiples and submultiples: converting mph and kmh

Meter per second and foot per second often leave space for two of the most commonly used units of measurement of speed: the kilometer per hour (kmh) and the mile per hour (mph). Perfectly suited to measure the speed of vehicles (both on land, sea, and air), it's not ideal for movements perceived as slow by humans or astronomical speeds.

Let's see how to convert speed between units. First, how the conversion to mph and kmh, from their previously introduced relatives:

\begin{align*} 1\ \text{km}/\text{h} = 0.2778\ \text{m}/\text{s}\\ 1\ \text{mph} =1.4667\ \text{ft}/\text{s} \end{align*}

To calculate the conversion of speed between kilometers per hour and miles per hour and vice versa, use the following formulas:

\begin{align*} 1\ \text{km}/\text{h} = 0.6214\ \text{mph}\\ 1\ \text{mph} =1.6093\ \text{km}/\text{h} \end{align*}

This conversion is the reason the acceleration of a car is measured with the time required for it to reach $60\ \text{mph}$: this value roughly corresponds to $100\ \text{km}/\text{h}$, a slightly more meaningful number!

## As fast as the wind: convert speed for meteorologists.

Humans have sailed the oceans of the world since the dawn of time. It doesn't come unexpected that two fields related to this practice, navigation and meteorology, have their own units of measurement for speed. Allow us to introduce the knot first.

The knot is a unit of speed equal to one nautical mile per hour. As you can see, it's not far from the definition of miles per hour; however, its origin is more interesting. Before the inventions of modern methods to assess the speed of a ship, sailors would use a rope with knots tied at a regular distance to measure how fast they were going. The method changed, but the name remained.

The conversion to knot from mph and kmh is:

\begin{align*} 1\ \text{km}/\text{h} = 0.54\ \text{kt}\\ 1\ \text{mph} =0.869\ \text{kt} \end{align*}

And to convert to mph and kmh from knots, we use the following equation:

\begin{align*} 1\ \text{kt} = 1.852\ \text{km}/\text{h}\\ 1\ \text{kt} =1.1508\ \text{mph} \end{align*}

Knots are used to measure both the speed of a vessel (or an aircraft) and the speed of the wind. Another measurement unit for wind, more strictly related to seafaring, is the Beaufort scale. This scale assigns a numeric value to the wind intensity according to its effect on sea or land. We have then:

• Beaufort number 0, corresponding to absence of wind;
• Beaufort number 1, corresponding to winds between $2\ \text{km}/\text{h}$ and $5\ \text{km}/\text{h}$ (slightly rippling the surface of the sea).

And so on. We meet our first strong wind at Beaufort number $7$, when it becomes hard to walk. From there, it rapidly progresses to damaging speeds. Beaufort numbers $11$ and $12$ are catastrophically strong winds, often associated with hurricanes and storms.

This characteristic gave the Beaufort scale a rather uncommon non-linear relationship to the other units of measurement of speed. And rightfully so! An increase of one “point” in the Beaufort scale between the values $1$ and $2$ doesn't compare to the interval between $9$ and $10$.

The relationship between meters per seconds and the Beaufort number is the following:

$v_{\text{m}/\text{s}}=0.836\cdot n_{\text{Beaufort}}^{\frac{3}{2}}$

This implies that Beaufort number $1$ corresponds to $0.836\ \text{m}/\text{s}$, Beaufort number $2$\$ to $2.3646\ \text{m}/\text{s}$. Beaufort number $9$ and $10$ are, respectively, $22.57\ \text{m}/\text{s}$ and $26.437\ \text{m}/\text{s}$ ($80\ \text{km}/\text{h}$ and $95\ \text{km}/\text{h}$).

To convert speed from Beaufort to other measurement units, pass through the meters per second: you will only have to remember one non-linear calculation for all the speed conversions.

## Faster!

The ultimate unit of measurement of speed is the speed limit of the universe: the speed of light. This universal constant, $c$, equals:

$c = 299,\!792,\!458\ \text{m}/\text{s}$

Though it is rarely used outside of physics, this huge number can help you with the perspective of things: for how fast we will ever go, a tiny particle will always outrun us.

## Speed orders of magnitude

Exploring the universe allows you to meet speeds of any kind, but with a limitation: speed is one of the few physical quantities with an upper bound: no known object can move at a speed higher than the speed of light, $c$.

The lowest speed we can imagine is... zero! While a zero length is hard to reconcile with physics (hence we introduced Planck's length, the smallest length with a physical meaning), a distance can be zero: simply don't move!

Skipping this seemingly trivial value, we can pin some significative values of speed:

• The speed of hair growth: $1.7\cdot10^{−8}\ \text{km}/\text{h}$, or $1.1\cdot10^{−8}\ \text{mph}$.
• The record speed of a snail: $0.0099\ \text{km}/\text{h}$, or $0.00615\ \text{mph}$.
• The top speed of Usain Bolt: $44.72\ \text{km}/\text{h}$, or $27.78\ \text{mph}$.
• The speed of sound in a standard atmosphere: $1,225\ \text{km}/\text{h}$, or $761\ \text{mph}$.
• The speed of Earth in its orbit: $107,280\ \text{km}/\text{h}$, or $66,700\ \text{mph}$.
• The maximum speed of an electron in a man-made experiment: $1,079,252,848.786\ \text{km}/\text{h}$, or $670,616,629.38\ \text{mph}$.

If you "invert" the speed measurement units, you obtain a measure of the time needed to cover a certain distance (in contrast with the distance covered in a given time): the pace. Humans think better in terms of the parameter we can easily control, the distance, but in races, biking, and other practices, the pace may be valuable information.

In our speed converter, we added one last section in which your speed gets converted to the corresponding pace: you will see many units there, too, from the minutes-seconds per mile (or kilometer) to the seconds needed to cover $100$ meters.

Davide Borchia
Imperial/US
mph
ft/s
yd/s
mi/s
Metric
km/h
m/s
km/s
cm/s
Other
knots
B
c
Pace
mins
sec / mile
sec / mile
min
sec / km
sec / 100m
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