Weight Equation
Weight is the gravitational force on an object. Unlike mass (which stays the same everywhere), weight changes with gravitational acceleration. On Earth, g ≈ 9.81 m/s²; on the Moon, g ≈ 1.62 m/s².
W = m × g
How It Works
Weight is the gravitational force on an object: W = m × g. Unlike mass (which stays the same everywhere), weight changes with gravitational acceleration. On Earth, g ≈ 9.81 m/s²; on the Moon, g ≈ 1.62 m/s². The same 70 kg person weighs 687 N on Earth but only 113 N on the Moon.
Example Problem
A 50 kg suitcase is placed on a scale at sea level on Earth. What is its weight in newtons?
- Identify the known values: mass m = 50 kg, gravitational acceleration g = 9.81 m/s² (standard Earth gravity).
- Determine what we are solving for: the weight W, which is the gravitational force on the suitcase.
- Write the weight equation: W = m × g.
- Substitute the known values: W = 50 kg × 9.81 m/s².
- Compute the result: W = 490.5 N (newtons).
- Convert for context: 490.5 N ≈ 110.2 lbf, roughly the effort to lift the suitcase on Earth.
A simpler example: a 10 kg backpack on Earth weighs 10 × 9.81 = 98.1 N.
When to Use Each Variable
- Solve for Weight — when you know mass and gravitational acceleration, e.g., finding the weight of an object on different planets.
- Solve for Mass — when you know weight and gravity, e.g., determining the mass of an object from a scale reading.
- Solve for Gravity — when you know weight and mass, e.g., calculating gravitational acceleration on an unknown planet.
Key Concepts
Weight is a force, not a property of matter. It results from gravity acting on mass and is measured in newtons (N) or pounds-force (lbf). Mass remains constant regardless of location, but weight changes with gravitational acceleration. This distinction matters in engineering, space science, and any context where g differs from Earth's standard 9.81 m/s².
Applications
- Structural engineering: calculating dead loads and live loads for building and bridge design
- Space exploration: determining equipment weight on the Moon, Mars, or in orbit for mission planning
- Elevator design: sizing motors and cables based on the maximum weight of passengers and cargo
- Laboratory measurements: converting between mass readings (grams) and weight (newtons) for force experiments
Common Mistakes
- Using mass units (kg) when weight units (N) are required — saying an object 'weighs 10 kg' is technically incorrect; it has a mass of 10 kg and weighs 98.1 N on Earth
- Assuming g is exactly 9.8 or 10 m/s² — the standard value is 9.80665 m/s², and actual gravity varies from 9.78 at the equator to 9.83 at the poles
- Forgetting that weight is zero in free fall — astronauts in orbit are weightless (free-falling around Earth) even though gravity still acts on them
Frequently Asked Questions
How do I find out how much something weighs on Earth or another planet?
Use the formula W = m × g. Multiply the object's mass in kilograms by the gravitational acceleration (9.81 m/s² on Earth). For example, a 70 kg person has a weight of 70 × 9.81 = 686.7 N on Earth.
What equation converts mass to weight?
The weight formula is W = m × g, where W is weight in newtons, m is mass in kilograms, and g is gravitational acceleration in meters per second squared. You can rearrange it to find mass (m = W / g) or gravity (g = W / m).
What is the difference between mass and weight?
Mass (kg) measures the amount of matter in an object and never changes. Weight (N) is the gravitational force on that mass and varies with location. A 70 kg person weighs 686.7 N on Earth but only 113.4 N on the Moon.
How much would I weigh on the Moon?
The Moon's gravitational acceleration is about 1.62 m/s², roughly one-sixth of Earth's 9.81 m/s². Multiply your mass in kg by 1.62 to get your lunar weight in newtons. A 70 kg person weighs about 113.4 N on the Moon versus 686.7 N on Earth.
Why do bathroom scales show kilograms?
Scales are calibrated assuming standard Earth gravity. They actually measure force (weight) but display the equivalent mass. In a different gravitational field — like on Mars — the reading would be wrong unless recalibrated.
What is the value of g on other planets?
Mars: 3.72 m/s². Jupiter: 24.79 m/s². Moon: 1.62 m/s². Venus: 8.87 m/s². A 70 kg person would weigh 260 N on Mars, 1,735 N on Jupiter, and 621 N on Venus.
Is weight a scalar or a vector?
Weight is a vector quantity — it has both magnitude and direction. Weight always points toward the center of the gravitational body (downward on Earth's surface). The W = mg formula gives the magnitude; the direction is always along the gravitational field line.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.
Weight Formula
The weight equation defines the gravitational force acting on an object:
W = m × g
Where:
- W — weight (gravitational force), measured in newtons (N)
- m — mass of the object, measured in kilograms (kg)
- g — gravitational acceleration, measured in meters per second squared (m/s²)
On Earth's surface, g averages 9.81 m/s² but varies slightly with latitude and altitude (9.78 at the equator to 9.83 at the poles). For other bodies: Moon 1.62 m/s², Mars 3.72 m/s², Jupiter 24.79 m/s².
Red = weight (W = mg)Blue = gravitational field (g)
Worked Examples
Space Exploration
How much does a Mars rover weigh on Mars?
The Perseverance rover has a mass of 1,025 kg. Mars has a gravitational acceleration of 3.72 m/s². What is the rover's weight on the Martian surface?
- W = m × g = 1,025 kg × 3.72 m/s²
- W = 3,813 N (about 857 lbf)
On Earth, the same rover weighs 10,055 N — nearly 2.6× more. Mission planners must account for this difference when designing landing systems.
Structural Engineering
What is the dead load of a concrete slab?
A reinforced concrete floor slab has a mass of 12,000 kg. Calculate the gravitational force (dead load) it exerts on the support beams.
- W = m × g = 12,000 kg × 9.81 m/s²
- W = 117,720 N (≈ 117.7 kN or 26,468 lbf)
Structural engineers must add safety factors (typically 1.2–1.4× for dead loads) when sizing beams and columns. This calculation gives the unfactored load.
Elevator Design
What mass can an elevator cable support?
An elevator cable has a maximum rated load of 25,000 N. Assuming standard Earth gravity, what is the maximum mass the cable can hold?
- Rearrange: m = W / g
- m = 25,000 N / 9.81 m/s²
- m ≈ 2,548.4 kg
This is the static limit. Dynamic loads during acceleration and deceleration increase the effective force, so elevator cables are rated well above the static maximum.
Weight on Other Planets
Gravitational acceleration varies across the solar system. Click a row to load it into the calculator with a 70 kg reference mass.
| Body | g (m/s²) | 70 kg Weight | Type |
|---|---|---|---|
| Mercury | 3.7 | 259 N | Rocky |
| Venus | 8.87 | 621 N | Rocky |
| Earth | 9.81 | 687 N | Rocky |
| Moon | 1.62 | 113 N | Moon |
| Mars | 3.72 | 260 N | Rocky |
| Jupiter | 24.79 | 1,735 N | Gas Giant |
| Saturn | 10.44 | 731 N | Gas Giant |
| Uranus | 8.87 | 621 N | Ice Giant |
| Neptune | 11.15 | 781 N | Ice Giant |
| Pluto | 0.62 | 43 N | Dwarf |
Surface gravity values are approximate averages. Actual values vary with altitude, latitude, and local geology.
Related Calculators
- Gravity Equations Calculator — calculate g at different altitudes and for different planets.
- Force Equation Calculator — general F = ma calculations.
- Density Calculator — find mass from density and volume.
- Specific Gravity Calculator — compare substance density to water.
- Mass Unit Converter — convert between kilograms, pounds, ounces, and grams.
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