# Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

# Inputs data - value and unit, which we're going to convert#

Value | ||

Unit | ||

Decimals |

# $1$ (kilometres per hour) is equal to:#

# metric#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

kilometres per hour | Show source$\frac{km}{h}$ | km/h | Show source$\text{...}$ | - | A velocity unit commonly used to measure the speed of land vehicles such as cars or trains. The vehicle moves at a speed of one kilometer per hour if it covers distance of one kilometre (1000 m) within one hour.$1\ \frac{km}{h} = \frac{1000\ m}{60\ min} = \frac{10\cancel{00}\ m}{36\cancel{00}\ s} = \frac{10}{36}\ \frac{m}{s}$ | Show source$...$ |

kilometres per minute | Show source$\frac{km}{min}$ | km/min | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit kilometer (km) and time unit minute (min). The body moves at a speed of one kilometer per minute if it travels a distance of one kilometer(1000 m) within one minute (60 s).$1\ \frac{km}{min} = \frac{100\cancel{0}\ m}{6\cancel{0}\ s} = \frac{100}{6} \frac{m}{s} = 16\ \frac{2}{3}\ \frac{m}{s}$ | Show source$...$ |

kilometres per second | Show source$\frac{km}{s}$ | km/s | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit kilometer (km) and time unit second (s). The body moves at a speed of one kilometer per second if it travels a distance of one kilometer (1000 m) within one second.$1\ \frac{km}{s} = \frac{1000\ m}{1\ s} = 1000\ \frac{m}{s}$ | Show source$...$ |

metres per hour | Show source$\frac{m}{h}$ | m/h | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit metre (m) and time unit hour (60 min). The body moves at a speed of one one metre per hour if it travels a distance of one meter (100 cm) within one hour (60 min).$1\ \frac{m}{h} = \frac{1\ m}{60\ min} = \frac{1\ m}{3600\ s} = \frac{1}{3600}\ \frac{m}{s}$ | Show source$...$ |

metres per minute | Show source$\frac{m}{min}$ | m/min | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit metre (m) and time unit minute (60 s). The body moves at a speed of one one metre per minute if it travels a distance of one meter (100 cm) within one minute (60 s).$1\ \frac{m}{min} = \frac{1\ m}{60\ s} = \frac{1}{60}\ \frac{m}{s}$ | Show source$...$ |

metres per second | Show source$\frac{m}{s}$ | m/s | Show source$\text{...}$ | - | Basic speed unit in the SI system. It was created by dividing length unit meter (m) and time unit second (s). The body moves at a speed of one meter per second if it covers a distance of one meter in one second (100 cm) | Show source$...$ |

# british-american#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

miles per hour | Show source$mph$ | mph | Show source$\text{...}$ | - | A speed unit commonly used in Anglo-Saxon countries. The vehicle moves at a speed of one mile per hour if it covers a distance of one mile (1 mi) within one hour.$1\ mph = \frac{1\ mi}{60\ min} = \frac{1\ mi}{3600\ s} = \frac{1}{3600}\ mps$ | Show source$...$ |

miles per minute | Show source$mpm$ | mpm | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit mile (mi) and time unit minute (min). The body moves at a speed of one mile per minute if it travels a distance equal to one mile (1 mi) within one minute (60 s).$1\ mpm = \frac{1\ mi}{1\ min} = \frac{1\ mi}{60\ s} = \frac{1}{60}\ mps$ | Show source$...$ |

miles per second | Show source$mps$ | mps | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit mile (mi) time unit second (s). The body moves at a speed of one mile per second if it travels a distance equal to one mile (1 mi) within one second.$1\ mps = \frac{1\ mi}{1\ s} = 1\ \frac{mi}{s}$ | Show source$...$ |

foot per hour | Show source$fph$ | fph | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit foot (ft) time unit second (s). The body moves at a speed of one foot per second if it travels a distance equal to one foot (1 ft) within one second.$1\ fps = \frac{1\ ft}{1\ s} = 1\ \frac{ft}{s}$ | Show source$...$ |

foot per minute | Show source$fpm$ | fpm | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit foot (ft) and time unit minute (min). The body moves at a speed of one foot per minute if it travels a distance equal to one foot (1 ft) within one minute (60 s).$1\ fpm = \frac{1\ ft}{1\ min} = \frac{1\ ft}{60\ s} = \frac{1}{60}\ fps$ | Show source$...$ |

foot per second | Show source$fps$ | fps | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit foot (ft) time unit second (s). The body moves at a speed of one foot per second if it travels a distance equal to one foot (1 ft) within one second.$1\ fps = \frac{1\ ft}{1\ s} = 1\ \frac{ft}{s}$ | Show source$...$ |

inch per hour | Show source$iph$ | iph | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit inch (in) time unit second (s). The body moves at a speed of one inch per second if it travels a distance equal to one inch (1 in) within one second.$1\ ips = \frac{1\ in}{1\ s} = 1\ \frac{in}{s}$ | Show source$...$ |

inch per minute | Show source$ipm$ | ipm | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit inch (in) and time unit minute (min). The body moves at a speed of one inch per minute if it travels a distance equal to one inch (1 in) within one minute (60 s).$1\ ipm = \frac{1\ in}{1\ min} = \frac{1\ in}{60\ s} = \frac{1}{60}\ ips$ | Show source$...$ |

inch per second | Show source$ips$ | ips | Show source$\text{...}$ | - | The derived unit of speed created by dividing length unit inch (in) time unit second (s). The body moves at a speed of one inch per second if it travels a distance equal to one inch (1 in) within one second.$1\ ips = \frac{1\ in}{1\ s} = 1\ \frac{in}{s}$ | Show source$...$ |

furlong per fortnight | Show source$-$ | - | Show source$\text{...}$ | - | Unit of speed in the furlong-firkin-fortnight system (FFF). FFF units were created for humorous purposes and the they are intentionally impractical to use. The body moves at the speed of one furlong per fortnight (furlong per two weeks) if it travels a distance equal to one furlong (1 fur) within two weeks.$1\ \frac{fur}{2\ tyg.} = \frac{1/8\ mi}{14\ dni} = \frac{1/8\ mi}{14 \times 24\ h} = \frac{1}{2688}\ mph$ | Show source$...$ |

# other#

Unit | Symbol | Symbol (plain text) | Value as symbolic | Value as numeric | Notes | Unit conversion formula |

speed of light in vacuum | Show source$c$ | c | Show source$\text{...}$ | - | The speed of light in a vacuum. Because it is the highest speed possible to achieve in nature, the speed given in this unit is always fractional (less or equal to one). $1\ c = 299 792 458\ \frac {m}{s}$ | Show source$...$ |

speed of sound in air (20°C, 1 atm) | Show source$-$ | - | Show source$\text{...}$ | - | The speed at which an acoustic wave travels in the air at temperature 20°C, under pressure of 1 atmosphere, which corresponds to three hundred and forty four meters per second. $V_{\text {sound air, 20°C, 1 atm.}} = 344\ \frac{m}{s}$ | Show source$...$ |

mach | Show source$M$ | M | Show source$\text{...}$ | - | A speed unit used among others in the aircraft. The body moves at the speed of one mach, if the acoustic wave traveling in the same medium would have the same speed. The speed of one mach in air at 15°C corresponds to 340.3 meters per second. $1\ M \text{(air, 15°C)} = 340.3\ \frac{m}{s}$ | Show source$...$ |

knot (nmi/h) | Show source$kn$ | kn | Show source$\text{...}$ | - | A speed unit used in sea transport and in some countries in aircraft. One knot corresponds to the speed of one nautical mile per hour.$1\ kt = 1\ \frac{inm}{h} = \frac{1\ inm}{1 h} = 1852\ \frac{m}{h}$ | Show source$...$ |

# Some facts#

- Velocity is a vector size.
- It specifies the
**change of the position vector**in time. The concept of velocity was formalized with the development of calculus. Since then, the velocity is defined as the**position vector derivative with time**i.e.:

$\vec{v} = \dfrac{\vec{dr}}{dt}$where:

- $\vec{v}$ is velocity vector,

- $\vec{r}$ is position vector,

- $t$ is time.

- $\vec{v}$ is velocity vector,
- In common parlance - when we use the word speed - we normally refer to
**the scalar size**, representing the value of the velocity vector (its "length"). - The velocity by definition only applies to singl point in time. Sometimes, in order to emphasize this fact (and rule out a possible confusion with the average speed) it is called
**instantaneous velocity**. - There is also concept of
**average velocity**, which is**ratio of distance to time**, in which this distance has been traveled. - Average velocity is sometimes colloquially called
**speed**, but it is not a phrase used by physicists. - The basic unit of velocity in the SI system is
**meter per second**:

$\dfrac{m}{s}$ - According to
**Einstein's theory of relativity**the highest attainable speed in nature is**the speed of light**amounting to 299 792 458 m/s.

- The speed of light constant exists in many physical formulas e.g. equation desribing
**the equivalence of energy and mass:**

$E=mc^2$

**Einstein's special theory of relativity**gives a more general sense of the speed of light as**limit velocity of energy transport**(or otherwise velocity of impact) in the universe..

- The light is electromagnetic wave with the frequency that is visible to the human eye. However, the speed of light concerns to all of electromagnetic waves and does not depend on their frequency. This means that for example radio or wifi signals are transmited with the speed of light.

- The speed of light constant exists in many physical formulas e.g. equation desribing
- Other common velocity constants are for example:

- First cosmic velocity - the smallest horizontal velocity to be given to the body relative to the celestial body attracts them to the body is moved along a closed orbit. In other words, it is the speed needed to
**became a satellite**.

- Second cosmic velocity - the velocity needed to "break free" from the
**gravitational attraction of the given orb**(for example Earth)..

- Third cosmic velocity - the initial velocity which a body has to have to
**leave the Solar System**.

- Fourth cosmic velocity - the initial velocity needed to
**leave the Milky Way**.

- First cosmic velocity - the smallest horizontal velocity to be given to the body relative to the celestial body attracts them to the body is moved along a closed orbit. In other words, it is the speed needed to

# How to convert#

**Enter the number to field "value"**- enter the NUMBER only, no other words, symbols or unit names. You can use dot (**.**) or comma (**,**) to enter fractions.

Examples:- 1000000
- 123,23
- 999.99999

**Find and select your starting unit in field "unit"**. Some unit calculators have huge number of different units to select from - it's just how complicated our world is...**And... you got the result**in the table below. You'll find several results for many different units - we show you all results we know at once. Just find the one you're looking for.

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# Ancient version of this site - links#

In December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.

Direct link to the old version: "Calculla v1" version of this calculator

Direct link to the old version: "Calculla v1" version of this calculator