How Find the Weight of an Object Using Mass and Gravity

Learn the formulas and techniques for calculating weight from mass

Co-authored by Sean Alexander, MS and Johnathan Fuentes

Last Updated: December 11, 2024 Fact Checked

If you’re taking a physics class, you’ll probably be asked to calculate weight from mass. But how do you do this, exactly? We’ve got you covered. While it sounds tricky, calculating weight from mass is very straightforward if you know which formula to use. This article will teach you that formula, plus how to use it when you encounter physics problems in class. As a bonus, we’ve included some practice problems to help these concepts sink in. Keep reading to learn how to calculate weight from mass on your next physics quiz, test, or homework assignment.

What is the formula for weight?

Use the formula $w=m*g$ to calculate weight from mass. In this formula, $w$ = weight (in N), $m$ = mass (in kg), and $g$ = acceleration due to gravity (in m/s²).

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Weight from Mass Calculator

Part 1

Part 1 of 3:

Calculating Weight

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Use the formula $w=m*g$ to convert weight into mass. Weight is defined as the force of gravity on an object. Scientists put that sentence into an equation by writing $w=m*g$ $w=m*g$ , or $w=mg$ $w=mg$ .^{[1]
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- Since weight is a force, scientists also write the equation as $F=mg$ .
- $F$ = symbol for weight, measured in Newtons, N.
- $m$ = symbol for mass, measured in kilograms, or kg.
- $g$ $g$ = symbol for gravitational acceleration, expressed as m/s², or meters per second squared.
  - If you're using meters, the gravitational acceleration at the Earth's surface is 9.8 m/s². Always use m/s² for acceleration, unless you’re instructed to do otherwise.
  - If you're asked to use feet, instead of meters, the gravitational acceleration on Earth is 32.2 ft/s². This is the same unit, it's just converted from meters to feet. Luckily, you’re very unlikely to encounter a problem with acceleration written in ft/s².
Determine the mass of the object. Because we're trying to get weight from mass, we can assume we already have the mass. Mass is the fundamental amount of matter an object has, and is expressed in kilograms.

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Determine the gravitational acceleration. In other words, figure out what $g$ $g$ is. On the surface of the Earth, $g$ $g$ is 9.8 m/s². Elsewhere in the universe, the acceleration of gravity is different.^{[2]
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- The gravitational acceleration on the moon is different from the gravitational acceleration on the Earth. Acceleration due to gravity on the moon is about 1.622 m/s², or about 1/6 of the acceleration that it is here on Earth. That's why you weigh 1/6 of your Earth-weight on the moon.^{[3]
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- The gravitational acceleration on the sun is different from the gravitational acceleration on the Earth and moon. Acceleration due to gravity on the sun is about 274.0 m/s², or about 28 times the acceleration that it is here on Earth. That's why you would weigh 28 times your Earth-weight on the sun (if you could survive!).^{[4]
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$Step 4 Plug the numbers into the equation F = m g {\displaystyle F=mg} .$

Now that you've got $m$ and $g$ , plug those values into the equation $F=mg$ . You’ll get a number described in Newtons, or N.

Part 2

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Sample Problems

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Example #1: An object has a mass of 100 kg. What is its weight on the surface of the Earth?
- We know $m$ equals 100 kg, and $g$ equals 9.8 m/s² (since this is the gravitational acceleration on Earth’s surface).
- Plug these values into the equation: $F$ = 100 kg * 9.8 m/s².
- $F$ = 980 N. In other words, on the surface of the Earth, an object with a mass of 100 kg will weigh about 980 Newtons on Earth.
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Example #2: An object has a mass of 40 kg. What is its weight on the surface of the moon?
- We know $m$ equals 40 kg, and $g$ equals 1.6 m/s² (since the gravitational acceleration on the Moon’s surface is 1.6 m/s²).
- Plug these values into the equation: $F$ = 40 kg x 1.6 m/s².
- $F$ = 64 N. In other words, on the surface of the moon, an object with a mass of 40 kg will weigh approximately 64 Newtons on the moon.
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Example #3: An object weighs 549 Newtons on the surface of the Earth. What is its mass?
- For this problem, we have to work backward. We have $F$ and $g$ , but we need to calculate $m$ .
- Set up the equation: 549 = $m$ * 9.8 m/s².
- Instead of multiplying $m$ * $g$ , we divide $F$ by $g$ . In other words, $m=F/g$ .
- Plugging in our values, we get $m$ = 549/9.8 m/s².
- $m$ = 56 kg. In other words, an object weighing 549 Newtons on the surface of the Earth will have a mass of about 56 kilograms.

Part 3

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Catching Mistakes

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Avoid confusing mass and weight. Remember that mass is the amount of "stuff" in an object, which stays the same no matter where you move it. Weight measures the force of gravity on that "stuff," which changes if you move through space. Try these mnemonic devices to help you memorize your units:
- Mass is in units of grams or kilograms. Both mass and gram contain an $m$ . Weight is in units of newtons. Both weight and newton contain a w.
- You only have weight while you're "wait"ing on Earth, but even "mass"tronauts have mass.
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Always use scientific units: kg, N, and m/s². Most physics problems use newtons (N) for weight, meters per second squared (m/s²) for gravitational force, and kilograms (kg) for mass. If you use a different unit for one of these values, your calculations will be incorrect. Convert all values to scientific units before plugging them into the standard equation. These conversions may help you out if you're used to the imperial / U.S. system:
- 1 pound-force = ~4.448 newtons
- 1 foot = ~0.3048 meters

Community Q&A

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How do I get the gravitational force and multiply it by the mass?

Community Answer

Gravitational force is proportional the two bodies' masses and the gravitational constant and is inversely proportional to the square of the distance between them. F= (m1 (Earth)*m2 (observed body)*G(constant))/r/r. G= 6.67408 × 10-11 m3 kg-1 s-2. However, for the sake of weight we usually take the gravitational accelration (g) which is equal to 9.81 m/s/s, usually rounded to 10 m/s/s. G (gravitational force/weight) = g (gravitational accelration) * m (mass of the observed body). If you use both methods, the two Gs should be equal barring some rounding errors.

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Does a scale measure weight or mass?

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It measures weight, because it measures the force gravity exerts on an object. But since we know what the gravitational constant is on Earth, we can convert that weight into mass (and many scales simply show the mass because they're calibrated to do so).

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If the mass of an object is 25kg on earth, what will be its weight on the moon?

Community Answer

The gravitational field strength of the moon is 1.6N/kg. This means that the weight of a 1kg mass object on the moon is 1.6N. Weight = mass x gravitational field strength Therefore, 25 kg multiplied by 1.6 N/kg, is 40 N.

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Addendum: Weights Expressed in kgf

A Newton is a SI-unit. Quite often the weight is expressed in kilogramforce or kgf. This is not a SI-unit, therefore less impeccable. But it is very convenient for comparing 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 the 101 kg astronaut is 101.3 kgf on the North Pole, and 16.5 kgf on the moon.
What is an SI-unit? It stands for Systeme International d'Unites, a complete metric system of units of measurement for scientists.

Tips

The most difficult part is understanding the difference between weight and mass as people tend to use the words 'weight' and 'mass' interchangeably. They use kilograms for weight, when they should use Newton, or at least kilogramforce. Even your doctor may discuss your weight, when he meant to discuss your mass.

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The gravitational acceleration g can also be expressed in N/kg. 1 N/kg = 1 m/s² exactly. So the numbers remain the same.

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An astronaut with a mass of 100 kg will weigh 983.2 N on the North Pole, and 162.0 N on the moon. On a neutron star, he'll weigh even more, but he probably won't notice.

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