The **weight** of an object is the force of gravity exerted on that object. The **mass** it is the amount of matter it has, and it is the same everywhere, regardless of gravity. That is why an object that has 20 kilograms of mass on Earth also has 20 kilograms of mass on the Moon, although it will weigh only 1/6 of that amount. It weighs 1/6 of its mass on the Moon, since the force of gravity on the Moon is 1/6 of the Earth. Read on for information and tips on calculating weight from mass.

## Steps

### Part 1 of 3: Calculate Weight

#### Step 1. Use the formula "w = m x g" to convert weight to mass

Weight is defined as the force of gravity on an object. The scientists put that sentence into an equation by writing **w = m x g**, or **w = mg**.

- Since weight is a force, scientists also write the equation as
**F = mg**. **F**= symbol of weight, measured in Newtons,**N**.**m**= symbol for mass, measured in kilograms or**kg**.**g**= symbol of gravitational acceleration, expressed in**m / s**, or meters per second squared.^{2}- If you use
**meters**, the gravitational acceleration of the Earth's surface is 9.8 m / s^{2}. This is the International Standard Unit ("SI") and the one you are probably using. - If you are using
**feet**because you have to, then the gravitational acceleration is 32.2 f / s^{2}. This is the same unit, only arranged differently to reflect feet instead of meters.

#### Step 2. Find the mass of an object

Since we are trying to find the weight from the mass, we know that we already have the mass. Mass is a fundamental amount of matter that an object has, and it is expressed in kilograms.

#### Step 3. Find the gravitational acceleration

In other words, find out the **g**. On the surface of the Earth, **g** is 9.8 m / s^{2}. In any other part of the universe, the acceleration of gravity changes. Your teacher must tell you, or the problem must indicate, where gravity is acting so you know.

- The gravitational acceleration of the Moon is different from that of the Earth. The acceleration due to the Moon's gravity is 1622 m / s
^{2}, or about 1/6 of the acceleration here on Earth. That is why on the Moon you weigh 1/6 of the weight you have on Earth. - The gravitational acceleration of the sun is different from the gravitational acceleration of the Earth and the Moon. The gravitational acceleration in the sun is about 274 m / s
^{2}, or 28 times the acceleration of the Earth. That is why in the sun you would weigh 28 times your weight on Earth.

#### Step 4. Write the numbers in the equation

Now that you have **m** and **g**, you can write those values into the equation **F = mg** and ready. You should get a number described in terms of Newtons, or **N**.

### Part 2 of 3: Sample Problems

#### Step 1. Solve sample question # 1

The question is: "An object has a mass of 100 kilograms. What is its weight on the surface of the Earth?"

- Have
**m**and**g**.**m**equals 100 kg, and**g**equals 9.8 m / s^{2}, since we are looking for the weight of the object on the surface of the Earth. - We write our equation:
**F**= 100 kg x 9.8 m / s^{2}. - This gives us the final answer. On the surface of the Earth, an object with a mass of 100 kg will weigh approximately 980 Newtons.
**F**= 980 N.

#### Step 2. Solve sample question # 2

Here's the question: “An object has a mass of 40 kilograms. How much does it weigh on the surface of the Moon?"

- Have
**m**and**g**.**m**equals 40 kg, and gravity is 1.6 m / s^{2}, since we are looking for the weight of the object on the surface of the Moon. - We write our equation:
**F**= 40 kg x 1.6 m / s^{2}. - This gives us the final result. On the surface of the Moon, an object with a mass of 40 kg will weigh approximately 64 Newtons.
**F**= 64 N.

#### Step 3. Solve sample question # 3

Here's the question: “An object weighs 549 Newtons at the surface of the Earth. What is its mass?"

- For this problem, we have to work backwards. We already have the weight
**F**and we have**g**. Now we need**m**. - Let's write our equation: 549 =
**m**x 9.8 m / s^{2}. - Instead of multiplying, we divide. Specifically, we divide
**F**Come in**g**. An object that weighs 549 Newtons at the surface of the Earth has a mass of about 56 kilograms.**m**= 56 kg.

### Part 3 of 3: Spot the Errors

#### Step 1. Avoid confusing mass and weight

The first mistake people make about these problems is confusing mass and weight. Remember that mass is the quantity of an object, which remains unchanged regardless of where you take it. The weight, for its part, measures the force of gravity exerted on that quantity and changes if you go out into outer space. Here are some mnemonic techniques to distinguish these units:

- Mass is measured in units of grams or kilograms. So much
**m**handle like gra**m**o contain the letter**m**. Weight is measured in newtons. So much pes**or**like newt**or**n contain the letter**or**. - You only have a fixed weight while on Earth, but even astronauts have a stable mass when in outer space.

#### Step 2. Use scientific units

Most physical problems use newtons (N) for weight, meters per second (m / s^{2}) for the force of gravity and kilograms (kg) for mass. If you use a different unit for any of these values, **will not be able** use the same formula. Convert the measurements to scientific units before replacing them into the standard equation. These conversions can help you if you usually use the imperial system of units:

- 1 pound-force = ~ 4.448 newtons
- 1 foot = ~ 0.3048 meters

#### Step 3. Expand the newtons to check your units

If you have a complex problem, keep track of the units while you search for the solution. Remember that 1 newton equals 1 (kg * m) / s^{2}. If necessary, perform the replacement to be able to cancel the drives.

- Example problem: Jorge weighs 880 newtons on Earth. What is its mass?
- Mass = (880 newtons) / (9.8 m / s
^{2}) - Mass = 90 newtons / (m / s
^{2}) - Mass = (90 kg * m / s
^{2}) / (m / s^{2}) - Cancel the units: mass = 90 kg
- Kg is the expected unit for mass, so you ordered the problem correctly.

## Appendix: Weight expressed in kgf

- A newton is an SI unit. Weight is often expressed in kilogram-force or kgf. This is not an SI unit; therefore, it is less perfect. But it is very convenient to compare weights anywhere with weights on Earth.
- 1 kgf = 9.8166 N.
- Divide the calculated number of Newtons by 9,80665, or use the last column when available.
- The weight of a 101 kg astronaut is 101.3 kgf at the North Pole, and 16.5 kgf on the Moon.
- What is an SI unit? It is a unit of the International System of Units, a metric system of units of measurement for scientists.

## Advice

- The hardest part is understanding the difference between weight and mass, as people tend to use both in the same way. They use kilograms for weight, when they should use Newtons, or at least kilogram-force. Even your doctor may be talking about your weight, when in fact he is referring to your mass.
- The gravitational acceleration g can also be expressed in N / kg. 1 N / kg = 1 m / s
^{2}exactly. So the number stays the same. - An astronaut with a mass of 100 kg will weigh 983.2 N at the North Pole and 162.0 N on the Moon. In a neutron star, it will weigh even more, but you probably won't be aware of it.
- Balances measure mass (in kg), while scales are based on compression or expansion of springs to measure your weight (in kgf).
- The reason Newton is preferred over kgf is because many other things are easily calculated when you know the number of Newtons.