Calculate Weight from Mass

The weight of an object is the force of gravity exerted on that object. The mass of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity. That's why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth. Read on for information about and tips on calculating weight from mass.

Steps

Weight from Mass Calculation Help

Doc:Weight from Mass Diagram,Weight from Mass Calculator

Calculating the Weight

  1. Use the formula "w = m x 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 x g, or
    w = mg.
    • 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 = 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. This is the standard international unit, and the one you should probably be using.
      • If you're using feet because you have to, the gravitation acceleration is 32.2 f/s2. This is the same unit, it's just rearranged to reflect feet instead of meters.
  2. Figure out the mass of an object. Because we're trying to get weight from mass, we know we already have mass. Mass is the fundamental amount of matter an object has, and is expressed in kilograms.
  3. Figure out the gravitational acceleration. In other words, figure out g. On the surface of the earth, g is 9.8 m/s2. Elsewhere in the universe, the acceleration of gravity changes. Your teacher should tell you, or the problem should indicate, where the gravity is acting from so that you know.
    • 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.
    • 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. Plug the numbers into the equation. Now that you've got m and g, you'll be able to plug those values into the equation F = mg and be ready to go. You should get a number described in terms of Newtons, or N.

Sample Problems

  1. Solve sample question #1. Here's the question: "An object has a mass of 100 kilograms. What is its weight on the surface of the earth?"
    • We have both m and g. m equals 100 kg, and g equals 9.8 m/s2, because we're looking for the weight of the object on the surface of the earth.
    • We set up our equation next: F = 100 kg x 9.8 m/s2.
    • 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.
  2. Solve sample question #2. Here's the question: "An object has a mass of 40 kilograms. What is its weight on the surface of the moon?"
    • We have both m and g. m equals 40 kg, and g equals 1.6 m/s2, because we're looking for the weight of the object on the surface of the moon this time.
    • We set up our equation next: F = 40 kg x 1.6 m/s2.
    • This gives us the final answer. On the surface of the moon, an object with a mass of 40 kg will weigh approximately 64 Newtons. F = 64 N.
  3. Solve sample question #3. Here's the question: "An object weighs 549 Newtons on the surface of the earth. What is its mass?"
    • For this problem, we have to work backwards. We already have F and we have g. We just need m.
    • Let's set up our equation: 549 = m x 9.8 m/s2.
    • Instead of multiplying, we divide. Specifically, we divide F by g. An object weighing 549 Newtons on the surface of the earth will have a mass of about 56 kilograms. m = 56 kg.

Catching Mistakes

  1. Avoid confusing mass and weight. The number one mistake people make on these problems is 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. Here's are a couple mnemonic to keep your units distinct:
    • 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.
  2. Use scientific units. 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, you cannot use the same formula. Convert 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
  3. Expand newtons to check your units. If you're working on a complex problem, keep track of the units as you work through your solution. Remember that 1 newton is equivalent to 1 (kg*m)/s2. If necessary, make that substitution to help you cancel out units.
    • Example problem: Jeffrey weighs 880 newtons on Earth. What is his mass?
    • mass = (880 newtons)/(9.8 m/s2)
    • mass = 90 newtons/(m/s2)
    • mass = (90 kg*m/s2)/(m/s2)
    • Cancel units: mass = 90 kg
    • Kg is the expected unit for mass, so you arranged the problem correctly.

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.
  • The gravitational acceleration g can also be expressed in N/kg. 1 N/kg = 1 m/s2 exactly. So the numbers remain the same.
  • 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.
  • Balances measure mass (in kg), while scales are based on compressing or expanding springs to measure your weight (in kgf).
  • The reason why the Newton is preferred above the kgf that seems so convenient is that a lot of other things are easier calculated when you know the number of Newtons.

Warnings

  • The expression 'atomic weight' doesn’t have anything to do with the weight of the atom, it’s a mass. This will probably not be changed, because 'atomic mass' is already in use for something slightly different.

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Sources and Citations

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