TFT

Gravitational Field Calculator – Calculate Gravitational Field Strength

Calculate the gravitational field strength at a distance from a mass. Our calculator uses g = GM/r² for point masses and spherical bodies.

How to Calculate Gravitational Field Strength

Step 1: Enter the mass of the celestial body in kilograms.

Step 2: Enter the distance from the center of the mass in meters.

Step 3: Click Calculate to see the gravitational field strength in N/kg or m/s².

Understanding Gravitational Fields

What Is Gravitational Field Strength

Gravitational field strength (g) tells you how strong gravity is at a specific point. It's measured in N/kg or m/s² - they're the same thing. On Earth's surface, g = 9.81 N/kg. That means every kilogram of mass experiences 9.81 newtons of gravitational force.

The Inverse Square Law

Gravity gets weaker with distance squared. Double your distance from a planet's center, and gravity drops to 1/4. Triple the distance, it drops to 1/9. This is why astronauts in the ISS (400 km up) still experience about 90% of Earth's surface gravity - they're only slightly farther from Earth's center.

Field Strength vs Force

Field strength is property of the location. Force depends on what you put there. A 1 kg mass at Earth's surface feels 9.81 N. A 10 kg mass at the same spot feels 98.1 N. The field strength (9.81 N/kg) is the same for both.

Gravitational Field Strength Reference
LocationField Strength (N/kg)Notes
Earth surface9.81Standard gravity
Moon surface1.621/6 of Earth's
Mars surface3.7138% of Earth's
Jupiter surface24.792.5x Earth's
Sun surface27428x Earth's
ISS orbit (400 km)~8.7Still 90% of surface

Gas giants don't have solid surfaces - values are at the 1 bar pressure level (sea level equivalent).

Frequently Asked Questions

What is the formula for gravitational field strength?
g = GM/r². G is the gravitational constant, M is the mass creating the field, r is distance from the center. For Earth, this gives 9.81 N/kg at the surface.
Why is gravitational field strength the same as acceleration?
Because F = ma and F = mg both describe gravitational force. Set them equal: ma = mg, so a = g. A falling object accelerates at exactly the field strength. That's why g is measured in both N/kg and m/s².
Does gravitational field strength change with altitude?
Yes. At 10 km altitude (cruising altitude for jets), g drops to about 9.77 N/kg - a 0.4% decrease. At the ISS altitude of 400 km, it's about 8.7 N/kg. You'd need to go much higher to see dramatic changes.
Why is gravity weaker on the Moon?
The Moon is much less massive than Earth - about 1.2% of Earth's mass. Even though it's also smaller (which would increase surface gravity), the mass effect dominates. Result: 1.62 N/kg vs Earth's 9.81 N/kg.
Can gravitational field strength be negative?
No. Field strength is always positive - it's the magnitude of the field. The direction is always toward the mass creating the field. We sometimes use negative signs in calculations to indicate direction, but the strength itself is positive.

Other Free Tools

Gravitational Force Calculator

Gravitational Force Calculator – Newton's Law of Gravitation

Escape Velocity Calculator

Escape Velocity Calculator – Calculate Escape Velocity

Orbital Period Calculator

Orbital Period Calculator – Calculate Orbital Period

Acceleration Calculator

Acceleration Calculator

Momentum Calculator

Momentum Calculator

Velocity Calculator

Velocity Calculator – Calculate Speed with Direction