In physics, weight is the force exerted on a mass by gravity. ISO 80000-3, the international standard for mechanical quantities, defines weight as the force that gives a body an acceleration equal to the local acceleration of free fall. NIST Special Publication 811 Chapter 8 reinforces this: the SI unit of weight in the scientific sense is the Newton (N), not the kilogram. Mass is a fixed property of matter, while weight changes depending on the strength of gravity in a given location. On Earth, a 70 kg person weighs approximately 686 Newtons. On the Moon, that same person weighs only about 113 Newtons because lunar gravity is roughly one-sixth of Earth's. This calculator uses the strict scientific definition of weight as a force, making it useful for physics coursework, engineering load calculations, and space mission planning.
What This Calculator Does
This calculator solves the weight formula for any one of its three variables. You can calculate:
- Weight (N): from mass and gravitational acceleration
- Mass (kg): from weight and gravitational acceleration
- Gravitational acceleration (m/s squared): from weight and mass
Gravity presets for Earth, Moon, Mars, Jupiter, and the Sun are provided for quick selection. The standard gravitational acceleration used is 9.80665 m/s squared, a value defined exactly by ISO 80000 and based on the 3rd General Conference on Weights and Measures (1901). This value remains current as of the 2022 CODATA adjustment, the latest available recommended values from NIST.
For related physics tools, try our BMI Calculator for health-related weight assessments, or our Force Calculator for general force calculations using Newton's second law. You can also use our Pressure Calculator to calculate force per unit area.
How the Calculation Works
Weight (W) = Mass (m) x Gravitational Acceleration (g)
Mass (m) = Weight (W) / Gravitational Acceleration (g)
Gravity (g) = Weight (W) / Mass (m)
Earth's standard gravitational acceleration is 9.80665 m/s squared, defined as an exact value by ISO 80000. It is commonly rounded to 9.81 or 9.807 for everyday calculations. This is a defined constant, not a measurement, so it has no uncertainty. Actual gravitational acceleration varies from about 9.78 m/s squared at the equator to 9.83 m/s squared at the poles due to Earth's rotation and non-spherical shape. The result in Newtons can be converted to pound-force (1 lbf = 4.44822 N) or kilogram-force (1 kgf = 9.80665 N).
How to Use the Calculator
- Select the variable you want to solve for using the tabs
- Enter the two known values
- Use a gravity preset or enter a custom gravitational acceleration
- The result appears instantly with additional unit conversions for weight
Example Calculations
Weight of a 70 kg Person on Earth
W = 70 kg x 9.80665 m/s squared = 686.47 N. This equals about 154.3 lbf or 70 kgf. The kgf equals the Newton value divided by standard gravity, which is why kilogram-force is sometimes called "kilogram-weight" in older engineering literature.
Weight on the Moon
The same 70 kg person on the Moon: W = 70 x 1.620 = 113.4 N, which is about 25.5 lbf. The astronaut feels much lighter but has the same mass. This is why astronauts could lift heavy equipment on the Moon that would be impossible to move on Earth.
Real-World Scenarios
Structural Engineering in Chicago
A structural engineer in Chicago is calculating the load on a floor beam in a new office building. The beam must support the weight of people, furniture, and the floor itself. She knows the total mass of these objects is 1,200 kg. Using the calculator with Earth's standard gravity, she finds W = 1,200 x 9.80665 = 11,768 N, or approximately 11.77 kN. This force value goes directly into her structural load calculations. Mass alone is insufficient for structural engineering because building codes specify loads in force units (Newtons or pounds-force), not mass units.
Space Mission Planning in Houston
A mission planner at a space company in Houston is calculating fuel requirements for a Mars lander. Equipment that weighs 1,000 N on Earth weighs only 378 N on Mars (using Mars gravity of 3.720 m/s squared). This means the lander's descent thrusters need significantly less force to control the descent on Mars than on Earth. She uses the calculator to convert the mass of each equipment item to weight on Mars, then sums the total to determine the thrust budget. The gravity preset for Mars eliminates the need to look up and manually enter the Martian gravitational acceleration.
Physics Education in Phoenix
A high school physics teacher in Phoenix uses the calculator during a lesson on Newton's laws of motion. He asks students to calculate their own weight in Newtons, then on the Moon, Mars, and Jupiter. A student who masses 55 kg discovers she weighs 539 N on Earth, 89 N on the Moon, 205 N on Mars, and 1,392 N on Jupiter. The dramatic difference between Earth and Jupiter (nearly 3 times heavier) helps students internalize that weight depends on gravity while mass stays constant. NIST SP 811 notes that this distinction is one of the most commonly confused concepts in introductory physics.
Common Mistakes to Avoid
- Treating mass and weight as identical: A 10 kg object weighs 98.07 N on Earth. Using 10 as the weight in Newtons would give wrong results. NIST SP 811 explicitly warns that in scientific and technical contexts, weight means force, not mass. In everyday commerce, "weight" means mass, which is why scales display kilograms
- Using the wrong gravity value: Earth's standard gravity is 9.80665 m/s squared exactly. It varies from about 9.78 at the equator to 9.83 at the poles. For precision work at a specific location, use the local gravitational acceleration rather than the standard value. The standard value is a defined constant for metrological purposes, not a measurement of actual gravity at your location
- Confusing lbf and lb: Pound-force (lbf) is a unit of force. Pound (lb) is a unit of mass in everyday use. In the imperial system, an object with a mass of 1 lb exerts a weight of approximately 1 lbf on Earth due to how the system is defined. This coincidence causes widespread confusion but only holds at standard gravity
- Forgetting that weight changes with location: Your mass is the same everywhere in the universe, but your weight changes depending on the local gravitational field. A 70 kg person weighs 686 N on Earth, 113 N on the Moon, and 274 N on Mars. Always specify the gravitational context when reporting weight
Limitations of This Calculator
This calculator uses the standard gravitational acceleration of 9.80665 m/s squared for Earth, which is a defined constant. Actual gravitational acceleration varies by approximately 0.5% across Earth's surface due to latitude, altitude, and local geology. For precision scientific work, use the local gravitational acceleration measured at your specific location. The calculator does not account for buoyancy effects, which NIST SP 811 notes are usually excluded from weight definitions but can matter in high-precision metrology. The presets for Moon, Mars, Jupiter, and the Sun use approximate gravitational accelerations and do not account for variations across those bodies. The calculator does not handle relativistic effects, which become significant at velocities approaching the speed of sound or in strong gravitational fields. For general physics, engineering, and education, the standard values provided here are sufficient.
Authoritative Research and Resources
- NIST Special Publication 811, Chapter 8: Weight - The official U.S. guide for the SI system, defining weight as a force measured in Newtons and explaining the distinction between scientific weight (force) and everyday weight (mass). NIST explicitly states that the SI unit of weight in the scientific sense is the Newton.
- NIST CODATA Recommended Values of Fundamental Physical Constants (2022) - The latest internationally recommended values for physical constants, including the standard gravitational acceleration. The 2022 adjustment is the seventh in the CODATA series. The next adjustment (2026) closes December 31, 2026 with results available early 2027.
- ISO 80000 Standard Gravity (9.80665 m/s squared) - The international standard defining standard gravitational acceleration as an exact value, established by the 3rd General Conference on Weights and Measures in 1901 and confirmed in ISO 80000. This defined constant has no uncertainty.