How to Calculate Weight (W = mg): Mass vs Force

Calculate weight with W = mg. Mass vs weight, g = 9.8 vs 10, worked examples, and a free weight calculator.

What Weight Asks

Weight is the gravitational force on an object. Mass tells you how much matter you have; weight tells you how hard gravity pulls on that matter. Same backpack on Earth and the Moon has the same mass but different weight.

Near Earth’s surface the formula is W = m g. Mass m in kilograms times gravitational field strength g (usually 9.8 m/s² or N/kg) gives weight in newtons (N).

If you already have m and g (or W and one unknown), open the free weight calculator first, then return here for mass-vs-weight traps and links to normal force and buoyancy.

The Formulas

  • W = m g — weight from mass and g.
  • m = W / g — rearrange for mass.
  • g = W / m — rearrange for field strength.

    • Use the g value your worksheet or exam gives (9.8, 9.81, or 10). Do not mix two different g values in one problem.

    Mass vs Weight

  • Mass (kg) is the same everywhere in ordinary classroom problems.
  • Weight (N) changes if g changes — Moon, other planets, or free fall contexts.
  • Never put kilograms into a force equation that expects newtons without converting with g.

    • On a flat floor with no other vertical forces, normal force equals weight: N = mg. See the normal force calculator and the

    normal force guide.

    Weight, Force, and Buoyancy

    Weight is a force, so it fits Newton’s second law when gravity is the net force: F = ma with a = g. Use the force calculator for F = ma in general.

    Float or sink compares object weight W = mg to buoyant force Fb = ρVg. See buoyancy and

    Archimedes’ guide.

    Units

  • m → kg.
  • g → m/s² or N/kg (same numeric value).
  • W → newtons (N). 1 N = 1 kg·m/s².
  • If mass is given in grams, convert to kilograms first (÷ 1000).

    • Worked Examples

    Example 1: 5.0 kg on Earth

    g = 9.8 m/s². W = m g = (5.0)(9.8) = 49 N downward.

    Example 2: find mass from weight

    W = 98 N, g = 9.8. m = W/g = 98/9.8 = 10 kg.

    Example 3: g = 10 estimate

    m = 2.5 kg, g = 10. W = 25 N — common when the paper allows g = 10.

    Example 4: same mass, different g

    m = 60 kg. Earth (g = 9.8): W = 588 N. Moon-like g = 1.6: W = 96 N — mass unchanged.

    Common Mistakes

  • Treating kilograms as newtons inside force or buoyancy problems.
  • Putting weight (N) into the mass slot of F = ma or PE = mgh.
  • Forgetting that weight is a downward force, not a scalar mass label.
  • Using Earth g on another planet or in orbit without adjusting.

    • Check It on the Calculator

    Weight calculator — W = mg.

    Force calculator.

    Normal force calculator.

    Buoyancy force calculator.

    Learn W = mg and confirm every homework number on the calculator.

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