# Measurement Converter

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD
Last updated: Nov 04, 2022

With Omni's measurement converter, you will learn every scientist's technique to convert between units when they really can't remember that conversion factor!

Keep reading: you will discover a universal tool to help you with the calculations to convert measurement units, both simple and composite. We will give you examples of how to convert measurement even if you don't know all the conversion factors and hopefully give you a way to navigate your way into science with a bit less difficulty!

## Units of measurement: the scale of reality

At the root of the fabric of reality, there are quantities: length, time, mass, and so on. Regardless of where you are in the Universe, if the law of physics is the same, a quantity associated with an object will remain the same.

🙋 If the physics is the same here and on a planet in the Andromeda galaxy, Tim, $1.70$ meters tall by $62$ kilograms on Earth, will still be $1.70$ meters tall by $62$ kilograms!

What can change is the way we measure those quantities. In reporting the value of a length, mass, time, etc., we decide to which measurement unit we want to compare the quantity.

🙋 Tim is $1.70$ meters tall, but for the inhabitants of the planet he landed, he is $0.89$ 🔹. The quantity is the same; however, Tim's new friend uses that weird unit (🔹) to measure it.

Units and their choice depend on many factors. We can have "human" units, like the foot, or "scientific" units, like the angstrom. They both measure length, but one is suitable for a person's height, the other for interatomic distance.

We feel like we are venturing too much into philosophical territory. Let's remain in science and discover how to convert measurement units!

## How to convert measurement units: technique and examples

The calculations to convert measurements are of fundamental importance in our daily lives. We do it constantly without even thinking. If someone says, "see you in half an hour", we know he is saying, "see you in thirty minutes": this way, we know at which minute we need to leave to get that bus!

From time to time, you can convert measurements in the blink of an eye: a meter is $100$ centimeters; hence the formula for the conversion is:

$N\ \mathrm{m} = N \times 100\ \mathrm{cm}$

Just add a couple of zeros, and it's done. The number $100$ is the conversion factor. Let's see a generic case!

⚠️ The following steps hold if your measurement units are directly proportional and can't be used if an arbitrary constant is added (for example, in the conversion between Celsius and Fahrenheit)!

Take the unit $A$ and the unit $B$. They are related through the conversion factor $k$ with the formula:

$1\ [A] = k\ [B]$

We can calculate the measurement converting factor in the other direction by finding the multiplicative inverse of $k$:

$1\ [B] = \frac{1}{k}\ [A]$

Now you can convert between any amount of $A$ and $B$:

$N\ [A] = N \times k\ [B]$

And vice-versa:

$N\ [B] = N\times \frac{1}{k}\ [A]$

That's it for this simple conversion. In the next section, we will discover the chain rule that will allow you to convert measurement units in (almost) every possible situation.

## The chain rule for the conversion of measurement units

When describing a phenomenon where more than two quantities appear, for example, a speed (where we measure both the length and the time), we use a composite measurement unit. Regarding the speed, we use meters per second or miles per hour. The word per in the unit means that we are dividing these quantities. Omitting it (as in the torque measurement unit Newton meter, or in the unit used by the fictional astronaut Mark Watney in The Martian, the pirate-ninja) implies that we are multiplying the units.

Converting between composite units is slightly trickier: to do so, we use the chain rule. The chain rule uses a fractional representation of the measurements conversion. In particular, a fraction that has value $1$ if we consider the measurement units:

$\frac{1000\ \mathrm{m}}{1\ \mathrm{km}} = 1$

This fraction represents a conversion factor, and since it has value $1$, we can multiply it by a value and, without changing the quantity we are measuring, change its units.

Let's see an example!

Say that you want to convert $50$ meters per second to miles per hour. Follow these steps with us!

1. Find the conversion factor between the measurement units at the numerator of the fraction. In our case, between meters and miles: $1\ \mathrm{mi}= 1609.3\ \mathrm{m}$. In fractional form, we write $1\ \mathrm{mi}/1.609.3\ \mathrm{m}=1$
2. Multiply the quantity in meters per second by this fraction. Simplifying the meters and multiplying the values, you'll find the rather unwieldy miles per second measurement unit: $50\ \mathrm{m/s} \times 1/1.609.3\ \mathrm{mi/m}=0.031\ \mathrm{mi/s}$
3. Find the conversion factor between the measurement units at the denominator, seconds and hours: $1\ \mathrm{h} = 3600\ \mathrm{s}$ or, in fraction, $3600\ \mathrm{s}/1\ \mathrm{h}$.
4. Multiply the previous result by this fraction. As you can see, in both cases, we chose the fraction with the desired measurement unit on the correct side of the line (miles at the numerator, hours at the denominator): $0.031\ \mathrm{mi/s} \times 3600/1\ \mathrm{s/h} = 111.6\ \mathrm{mi/h}$.
5. You converted measurements between meters per second and miles per hour without knowing the conversion factor! Congrats!

The procedure above will be even more straightforward with a formula:

$\begin{split} 50&\ \frac{\mathrm{m}}{\mathrm{s}} \\[1em] &\!\!=50 \frac{\cancel{\mathrm{m}}}{\cancel{\mathrm{s}}} \!\times \!\frac{1\ \mathrm{mi}}{1609.3\ \cancel{\mathrm{m}}} \!\times \!\frac{3600\ \cancel{\mathrm{s}}}{1\ \mathrm{h}} \\[1em] &\!\!= 111.6\ \frac{\mathrm{mi}}{\mathrm{h}} \end{split}$

Now we can learn how to convert measurements in the case of multiplication and division of quantities.

Define the following pair of measurement units:

• $1\ [A] = k\ [C]$; and
• $1\ [B] = h\ [D]$.

Write the unit fractions:

$\frac{1\ [A]}{k\ [C]}=\frac{k\ [C]}{1\ [A]} = 1$

And:

$\frac{1\ [B]}{h\ [D]}=\frac{h\ [D]}{1\ [B]} = 1$

Now consider the measurement unit $[A\cdot B]$. We can convert it into another one measuring the same quantity, $[C\cdot D]$. How?
Apply the chain rule!

$\begin{split} N&\ [A\cdot B] \\ &= N\ [A\cdot B]\times \frac{k\ C}{1\ A} \times \frac{h\ D}{1\ B} \\ &= N\times k\times h\ [C\cdot D] \end{split}$

A similar reasoning holds if you want to convert between $A$ per $B$ ($[A/B]$) and $C$ per $D$ ($[C/D]$). Look at how we chose the unit fractions:

$\begin{split} N&\ [A/B] \\ &= N\ [A/B]\times \frac{k\ C}{1\ A} \times \frac{1 B}{h\ D} \\ &= \frac{N\times k}{h}\ [C/D] \end{split}$

That's it!

## How to use Omni's measurement converter

Using Omni's measurement converter is super easy, barely an inconvenience! Choose the type of units you are converting: single units, multiplied, or divided.

Then insert the correct conversion factors. You will need to insert only half of them; we can calculate the others.

Last, but not least, insert the value you need to convert. If you need to know only the comprehensive factor, type $1$!

Example? Example!

Say that you want to convert between measurement units of pace. A commonly used one is the minutes per kilometer. We want to know our pace in second per meter. How do we do that?

1. Choose "division" in the first field.
2. We will use $A$ as minutes, and $B$ as kilometers. On the other hand, $C$ will be seconds and $D$ meters.
3. Insert the proper conversion factors:
• $1\ A = 60\ C$; and
• $1\ C = 1000\ D$.
4. Insert the pace in the field $A/B$. Say you need 15 minutes to walk a kilometer.
5. The answer is $0.9$. This means you need $0.9$ seconds to walk a meter!

## Other tools to help you with the conversion of measurement units

Conversion is not an easy matter, and we at Omni know this! That's why we offer you a complete set of conversion tools you can use whenever you need them. Apart from this handy measurement converter, you can try the following:

## FAQ

### How do I convert between two measurement units?

You need to know the conversion factor to convert between two measurement units. The conversion factor between the units A and B is the number k that satisfies the following equation:
1 A = k B
Multiplying a quantity expressed in A by k gives us the same amount in B.

Notice that 1/k is the conversion factor for the inverse conversion from B to A.

### How do I convert from meters per second to feet per hour?

To convert between meters per second and feet per hour, follow the next steps:

1. Define the fraction with the value 1 between meters and feet: 3.281 ft/1 m = 1.
2. Define the fraction between seconds and hours: 3600 s/1 h = 1.
3. Multiply your quantity in meters per second by the two fractions to find the quantity in feet per hour:
N m/s = N × 3.281 ft/1 m × 3600 s/1 h = M ft/h

### How do I find the conversion factor of a composite measurement unit?

A composite measurement unit's conversion factor results from the corresponding mathematical operation between the individual conversion factors.

• If you are multiplying measurement units (as in N m, for the torque), multiply the conversion factors.
• If you are dividing (as in m/s or km/h), divide the conversion factors.

### How much is 1 L/h in gallons per day?

A liter per hour is equal to 6.34 gallons per day. To find this value, we:

1. Found the conversion between gallons and liters: 1 L = 0.264 gals.
2. Found the conversion between days and hours: 1 d = 24 h.

3 Multiplied the quantity 1 L/h by the following unit fractions: 0.264 gal/1 L and 24 h/1 d:
1 L/h × 0.264 gal/1 L × 24 h/1 d = 6.34 gal/d

Davide Borchia
Type of unit
Type
Single unit ([A] → [B])
Conversion factors
1 A =
B
1 B =
A
Conversion
A
B
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