Mass and weight are different: mass is a fixed property of an object measured in kilograms; weight is a gravitational force measured in newtons that changes with location. Getting this distinction right is one of the most common mark-earners in GCSE physics exams.
What is mass?
Mass is the amount of matter in an object. It is:
- Measured in kilograms (kg)
- A scalar quantity (it has magnitude only, no direction)
- Constant — mass does not change regardless of where in the universe an object is located
A 70 kg person has a mass of 70 kg on Earth, on the Moon, in deep space, and on Jupiter. Mass cannot be changed by moving to a different location.
What is weight?
Weight is the gravitational force acting on an object. It is:
- Measured in newtons (N)
- A vector quantity (it has both magnitude and direction — always towards the centre of the gravitational body)
- Dependent on gravitational field strength — weight changes with location
The same 70 kg person weighs 686 N on Earth, about 115 N on the Moon, and about 1,629 N on Jupiter. Their mass has not changed; only the gravitational field acting on them has changed.
What is gravitational field strength?
Gravitational field strength (g) is defined as the force of gravity per unit mass:
g = W / m
Or rearranged: W = m × g
| Symbol | Quantity | Unit |
|---|---|---|
| W | Weight | Newton (N) |
| m | Mass | Kilogram (kg) |
| g | Gravitational field strength | Newton per kilogram (N/kg) |
On Earth's surface, g = 9.8 N/kg (sometimes approximated as 10 N/kg in calculations). This means every kilogram of mass experiences 9.8 N of gravitational force.
Gravitational field strength decreases with distance from the centre of a massive object. At the top of a mountain g is very slightly less than at sea level; in orbit g is lower still (but not zero — astronauts are weightless in orbit because they are in free fall, not because g = 0).
Gravitational field strengths across the solar system
| Location | g (N/kg) | Weight of 60 kg person (N) |
|---|---|---|
| Earth's surface | 9.8 | 588 |
| Moon's surface | 1.6 | 96 |
| Mars's surface | 3.7 | 222 |
| Jupiter's surface (cloud tops) | 24.8 | 1,488 |
| Sun's surface | 274 | 16,440 |
| Deep space (negligible g) | ≈ 0 | ≈ 0 |
How do you calculate weight?
Use the equation: W = m × g
Worked example 1:
Calculate the weight of a 25 kg bag on Earth (g = 9.8 N/kg).
W = m × g = 25 × 9.8 = 245 N
Worked example 2:
An astronaut has a mass of 80 kg. Calculate their weight on the Moon (g = 1.6 N/kg).
W = m × g = 80 × 1.6 = 128 N
Their mass is still 80 kg on the Moon — only their weight has changed.
Worked example 3 (rearranging):
An object weighs 490 N on Earth (g = 9.8 N/kg). Calculate its mass.
m = W / g = 490 / 9.8 = 50 kg
How does a spring balance (newton metre) measure weight?
A spring balance (newton metre) measures weight directly in newtons — it measures the force with which gravity pulls an object. The spring stretches by an amount proportional to the force (Hooke's law), and the scale is calibrated in newtons.
A mass balance (like a beam balance or kitchen scales) compares masses — it would give the same reading on the Moon because both sides experience the same reduction in g.
This is why astronauts on the Moon weigh less on a spring balance (gravity is weaker, so the spring stretches less) but read the same on a beam balance.
Frequently asked questions
Why do astronauts float on the International Space Station if gravity still acts there?
At the ISS's orbit (about 400 km above Earth), g ≈ 8.7 N/kg — gravity is still quite strong, around 89% of its surface value. Astronauts appear to float because the ISS is in free fall — it is continuously falling towards Earth while moving forward fast enough that Earth's surface curves away beneath it. Both the astronauts and the station fall together at the same rate, so the astronauts feel no contact force from the floor. This is true weightlessness from the astronauts' experience, but it is caused by free fall, not by the absence of gravity.
Why does weight change but mass stay the same?
Mass is a fundamental property of matter — it represents the quantity of atoms and their masses, which do not change with location. Weight is a force caused by the interaction between that mass and a nearby massive object (Earth, the Moon, etc.). Different massive objects produce different gravitational fields, so the force they exert on the same mass varies. Moving an object to the Moon does not change the number or type of atoms in it; it only changes the strength of the gravitational pull.
How do scientists measure gravitational field strength precisely?
The most accurate measurements of g use a freely falling object and measure the rate of acceleration using laser interferometry or high-precision timing. Because W = mg and F = ma from Newton's second law, the gravitational field strength equals the acceleration of free fall when only gravity acts: g = 9.81 m/s² (in consistent SI units) = 9.81 N/kg. These are equivalent because 1 N = 1 kg m/s², so N/kg simplifies to m/s². In practice g varies slightly across Earth's surface due to altitude, the Earth's rotation, and local geology.
Is it wrong to say someone "weighs 70 kilograms"?
In everyday speech, "I weigh 70 kg" is universally understood, but it is scientifically inaccurate. The person's mass is 70 kg; their weight is approximately 686 N on Earth. The confusion arises because kilograms are used in everyday life for what is actually mass, and "weight" is used informally to mean mass. In physics exams, always use the correct terms: mass in kg and weight in N. Examiners will penalise answers that confuse the two.
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