The Acceleration Due to Gravity Calculator computes surface gravitational acceleration for any planet from mass and radius using g = GM/R². Compare gravity across the solar system, calculate weight on other worlds, and explore how planetary size and density determine surface g.
9.819532
m/s²
1.001314
981.95
N
9.819532
m/s²
1.001314
981.95
N
The calculator for acceleration due to gravity determines the gravitational acceleration at the surface of any spherical body — planet, moon, or asteroid — from its mass and radius. This quantity, denoted g, governs the weight of objects, orbital mechanics near the surface, and the period of pendulums and springs on that body.
Surface gravitational acceleration is derived directly from Newton's law of universal gravitation applied at the surface:
g = GM / R²
where G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, M is the body's mass in kg, and R is its radius in meters. Earth's standard surface gravity of 9.80665 m/s² emerges from M = 5.972 × 10²⁴ kg and R = 6.371 × 10⁶ m. The gravitational force calculator extends this to force between any two masses, and the gravitational constant calculator explores the role of G in the formula.
Gravitational acceleration varies enormously across planetary bodies due to differences in mass and radius:
The weight on other planets calculator uses these values to convert Earth weight to other planetary surfaces. Use this online calculator for any body with known mass and radius, including exoplanets and asteroids.
Earth's surface gravity is not perfectly uniform — it varies by approximately 0.5% between equator and poles for three reasons. First, Earth is an oblate spheroid: the polar radius (6,357 km) is shorter than the equatorial radius (6,378 km), placing polar observers closer to Earth's center where gravity is stronger. Second, centrifugal acceleration from Earth's rotation reduces effective gravity at the equator by about 0.034 m/s². Third, local density variations in the crust produce gravity anomalies measured in milliGals. The acceleration converter translates g values between unit systems including the Gal used in geophysical surveys. The gravitation calculators category covers orbital mechanics and gravitational potential energy tools.
Enter the mass of the celestial body in kilograms and the radius (distance from center to surface) in meters. The calculator evaluates:
$$g = \frac{GM}{R^2}$$
It also computes the ratio to Earth's gravity: $$g_{\text{ratio}} = g / 9.81$$, and the weight of a 100 kg object on that surface: $$W = 100 \times g$$.
Note that $$g$$ depends on $$R^2$$ in the denominator, meaning that a body could have a lower mass than Earth but a higher surface gravity if its radius is sufficiently small (this is the case for white dwarf stars). Conversely, gas giants like Saturn have low surface gravity relative to their enormous mass because their radii are so large.
This formula assumes a spherically symmetric, non-rotating body. Real planets have slightly varying $$g$$ due to rotation (centrifugal effects), oblateness, and internal density variations.
A gravitational acceleration of $$9.81 \, \text{m/s}^2$$ corresponds to standard Earth gravity (ratio = 1.0). Values below 1 indicate weaker gravity — you would weigh less and could jump higher. Values above 1 indicate stronger gravity — movement becomes harder. For human long-term habitation, gravity below about 0.3g may cause serious health issues including bone density loss and muscle atrophy, while gravity above about 3g becomes physically debilitating for extended periods.
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Confirms the well-known value of g ≈ 9.82 m/s² for Earth. A 100 kg person weighs about 982 N (~220 lbs).
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Mars has about 38% of Earth's gravity. A 100 kg person would weigh only 373 N (~84 lbs) on Mars.
Earth's surface gravity varies from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. This is due to Earth's oblate shape (larger radius at the equator), centrifugal effects from rotation, and local variations in subsurface density (geological anomalies).
Gravity decreases with altitude because $$R$$ increases. At the International Space Station's orbit (~408 km altitude), $$g \approx 8.67$$ m/s². Astronauts experience weightlessness not because gravity vanishes but because they are in continuous free fall around Earth.
Among the solar system's planets, Jupiter has the highest surface gravity at approximately 24.79 m/s² (2.53g). Despite Saturn being nearly as massive, its much larger radius gives it a surface gravity of only 10.44 m/s² (1.06g).
Yes. If the object has a much smaller radius, $$g = GM/R^2$$ can be large even for modest mass. White dwarf stars, with masses comparable to the Sun compressed into Earth-sized volumes, have surface gravity roughly 100,000 times Earth's.
$$G$$ (capital) is the universal gravitational constant — a fixed value describing the strength of gravity everywhere. $$g$$ (lowercase) is the local gravitational acceleration at a specific location, which depends on the nearby mass and distance. They are related by $$g = GM/R^2$$.
No. The formula $$g = GM/R^2$$ gives the true gravitational acceleration without centrifugal correction. For rapidly rotating bodies, the effective surface gravity at the equator is reduced by the centrifugal term $$\omega^2 R$$, where $$\omega$$ is the angular velocity.
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