Weight Formula
The weight formula W = mg calculates the gravitational force on an object.
Learn how weight differs from mass with clear examples.
The Formula
W = mg
Weight is the force of gravity acting on an object. It equals mass multiplied by the gravitational acceleration.
Variables
| Symbol | Meaning |
|---|---|
| W | Weight (measured in newtons, N) |
| m | Mass of the object (measured in kilograms, kg) |
| g | Acceleration due to gravity (9.81 m/s² on Earth) |
Example 1
What is the weight of a 75 kg person on Earth?
Identify the values: m = 75 kg, g = 9.81 m/s²
Apply the formula: W = mg = 75 × 9.81
W = 735.75 N
Example 2
A crate weighs 196.2 N on Earth. What is its mass?
Rearrange the formula: m = W / g
Substitute: m = 196.2 / 9.81
m = 20 kg
When to Use It
Use the weight formula when you need to convert between mass and gravitational force.
- Calculating how much force gravity exerts on an object
- Converting mass (kg) to weight (N)
- Comparing weight on different planets (change g accordingly)
- Engineering and construction load calculations
Key Notes
- Mass ≠ Weight — mass is the amount of matter (the same on Earth, the Moon, and in space) while weight is the gravitational force, which varies by location
- On the Moon (g ≈ 1.62 m/s²), a 75 kg person weighs about 122 N — the same mass as on Earth, but only 1/6 the weight
- Everyday language uses "weight" in kilograms, which is technically mass — this works fine on Earth since g is nearly constant (9.78–9.83 m/s² from equator to poles)
- An object in orbit is not weightless — it is in free fall and experiences no normal force, but Earth's gravity is still acting on it
Key Notes
- Formula: W = mg: Weight is a force (newtons), not a mass (kilograms). g ≈ 9.81 m/s² on Earth's surface. A 70 kg person weighs 70 × 9.81 ≈ 686 N — but colloquially "weighs 70 kg" because we confuse weight and mass in everyday speech.
- Apparent weight in accelerating frames: In an elevator accelerating upward at a m/s², apparent weight = m(g + a). Accelerating downward: m(g − a). In free fall (a = g downward): apparent weight = 0 — weightlessness. This is what astronauts experience in orbit.
- g varies by location: g at the equator ≈ 9.780 m/s² (centrifugal effect + farther from Earth's center); at the poles ≈ 9.832 m/s². On the Moon: 1.62 m/s² (~1/6 Earth). On Mars: 3.72 m/s² (~3/8 Earth). Weight changes; mass does not.
- Normal force ≠ weight in general: Normal force equals weight (mg) only on a horizontal surface with no vertical acceleration. On an incline, the normal force = mg cosθ. In an elevator, normal force changes with acceleration. The two forces are equal only in the special case of static level ground.
- Applications: Weight calculations determine structural load requirements (floor loading, crane capacity), satellite orbital mechanics (weight is the centripetal force), scale calibration, rocket propulsion requirements (must overcome weight), and exercise physiology (relative strength per body weight).