Weight Calculator (W = mg)
Calculate weight from mass using W = mg, or find mass from a known weight. Uses Earth's standard gravity g = 9.8 m/s² with step-by-step working.
Weight is a force
Weight is not the same thing as mass — weight is the gravitational force pulling an object down, calculated as:
- W — weight, in newtons (N)
- m — mass, in kilograms (kg) — always positive
- g — acceleration due to gravity, 9.8 m/s² on Earth (a fixed constant here)
Enter the mass to get weight, or enter the weight to solve back for mass.
Worked example
What does a 10 kg object weigh on Earth?
- Formula: W = mg
- Substitute: W = 10 × 9.8
- Result: W = 98 N
Mass vs. weight
This distinction matters in everyday language ("how much do you weigh?" really means "what is your mass in kg, converted through Earth gravity into a weight?") and in physics problems that specify a different planet or moon.
Solving for mass
Given a weight of 98 N, the mass is found by dividing by g:
m = W / g = 98 / 9.8 = 10 kg
Common mix-ups
- Using kg as if it were the force unit. Kilograms measure mass; newtons measure weight (force). Don't report a weight in kg — convert with W = mg first.
- Forgetting g entirely. A common error is writing W = m instead of W = mg, which skips the gravity multiplication.
- Assuming g is universal. 9.8 m/s² is specific to Earth's surface — other planets, the Moon, and orbital environments have different values.
Where this shows up
Weight calculations appear in everyday unit conversions (kg readouts on a scale vs. the newtons used in physics), engineering load calculations, and any problem that asks for the gravitational force on an object. It's the special case of the general force calculator (F = ma) where acceleration equals gravity.
Frequently asked questions
- What is the formula for weight?
- Weight is W = mg, where W is weight in newtons (N), m is mass in kilograms (kg), and g is the acceleration due to gravity, 9.8 m/s² on Earth.
- What is the difference between mass and weight?
- Mass (kg) is the amount of matter in an object and never changes. Weight (N) is the force of gravity pulling on that mass, so it changes with location — the same 10 kg object weighs less on the Moon because the Moon's gravity is weaker.
- Why does this calculator use g = 9.8 m/s²?
- 9.8 m/s² is Earth's standard surface gravity, the value used in nearly all introductory physics problems. On another body (the Moon, Mars) the true weight would use that body's own gravitational acceleration instead.
- How do I find mass from a known weight?
- Rearrange the formula to m = W / g. Enter the weight and leave the mass field blank, and the calculator divides by 9.8 automatically.
- Can weight be negative?
- No — weight and mass must both be positive. Enter a negative weight (or a mass of zero or less) and the calculator returns a check-your-input message instead of a negative result, since neither quantity can be negative in the real world.
- How is weight related to force in general?
- Weight is a special case of Newton's second law, F = ma, where the acceleration is specifically gravity (a = g). See the [force calculator](/en/calculators/science/force) for the general F = ma relationship with any acceleration.