Formula of Weight: W = mg, Unit, Mass vs Weight, Examples

The formula of weight is $W = mg$ : an object's weight equals its mass multiplied by the local acceleration due to gravity. A 50 kg student on Earth, where g = 9.8 m/s², has a weight of 490 N.

Weight is a force, the pull of a planet on a body, so it is measured in newtons and points toward the planet's centre. Mass is the amount of matter and stays the same everywhere. Mixing up the two is a classic slip when studying the laws of motion. Type g = 9.8 into the calculator for Earth, or the value for another world.

Quick facts

Formula
$W = mg$
SI unit
newton (N)
Dimensional formula
[M¹ L¹ T⁻²]
Type
Vector, directed toward the centre of the Earth
g on Earth
9.8 m/s² (9.81 is also used)
g on the Moon
about 1.62 m/s², roughly one sixth

Weight formula physics: the symbols

Symbols in W = mg
Symbol	Meaning	SI unit
$W$	Weight, the gravitational force	N
$m$	How much matter the body holds	kg
$g$	Acceleration due to gravity, also the gravitational field strength in N/kg	m/s²

Notice that g has two equal readings. As an acceleration it is 9.8 m/s², the rate at which a dropped object speeds up. As a field strength it is 9.8 N/kg, the force on each kilogram. The units are identical, since 1 N/kg = 1 m/s².

Mass and weight are not the same

Mass compared with weight
Property	Mass	Weight
Meaning	Amount of matter, measure of inertia	Gravitational pull on that matter
Unit in SI	kilogram (kg)	newton (N)
Vector or scalar	Scalar	Vector
Changes from place to place	No	Yes, with g
Measured with	Beam balance	Spring balance

In daily life people say they weigh 50 kilograms. In physics, 50 kg is the mass and 490 N is the weight. Exam answers must keep them apart.

Worked examples using the formula of weight

Example 1: on Earth

Find the weight of a 50 kg student. Use g = 9.8 m/s².

$W = mg = 50 \times 9.8 = 490\ \text{N}$

Example 2: on the Moon

What does the same student weigh on the Moon, where g = 1.62 m/s²? What is the mass there?

$W = 50 \times 1.62 = 81\ \text{N}$

The mass is still 50 kg. Only the weight has dropped, to about one sixth.

Example 3: grams and kgf

A school bag has a mass of 750 g. Find its weight in newtons and in kilogram force.

Convert: 750 g = 0.750 kg. $W = 0.750 \times 9.8 = 7.35\ \text{N}$ .

Since 1 kgf = 9.8 N, the weight is 7.35 ÷ 9.8 = 0.75 kgf. In kgf the number matches the mass in kg, which is why that unit is easy to misuse.

How weight changes with height and place

g is not exactly the same everywhere on Earth. It is a little larger at the poles than at the equator, because Earth bulges at the equator and spins. It also falls as you go up. From $g = \frac{GM}{R^2}$ , at a height h small compared with Earth's radius R, $g_h \approx g\left(1 - \frac{2h}{R}\right)$ . The acceleration due to gravity formula page explains these changes, and the gravitational force formula page shows where W = mg comes from.

For a satellite in orbit the weight is not zero; gravity still pulls on it. The astronauts feel weightless because they and their craft fall together, so the floor pushes on them with no force.

Real weight and apparent weight

A bathroom scale does not measure W directly. It measures the normal force pushing up on your feet. In a lift accelerating upward at a, the scale reads $m(g + a)$ ; accelerating downward it reads $m(g - a)$ . Your true weight mg has not changed; only the scale reading has. The normal force formula page works these cases.

If a question says an object weighs 20 kg, it means a mass of 20 kg. Convert with W = mg before using the value as a force.

Slips with the weight formula

Giving weight in kg. A weight answer needs newtons. Write the unit N every time.
Skipping the gram conversion. 750 g must become 0.750 kg before you multiply by g.
Thinking weight vanishes in orbit. At the height of a low satellite, g is still close to 9 m/s².
Choosing your own g. Some boards allow 10 m/s² for quick arithmetic. Use whatever value the question states, and 9.8 m/s² if it states none.

Frequently asked questions

What is the formula of weight?

Weight equals mass times the acceleration due to gravity, W = mg. With m in kg and g in m/s², W comes out in newtons.

What is the SI unit of weight?

The newton (N). Kilograms measure mass, never weight.

Is weight a vector or scalar?

Weight is a vector. It points toward the centre of the Earth or of whichever body is doing the pulling.

Why is weight less on the Moon?

The Moon's gravitational field strength is about 1.62 N/kg, roughly a sixth of Earth's, so the same mass is pulled with about a sixth of the force.

What is the difference between mass and weight?

Mass measures how much matter a body contains and does not change from place to place. Weight depends on g as well, since it is gravity's pull on that mass.