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physics

Gravitational Field Strength Calculator

Calculate gravitational field strength g = G·M ÷ r² at any distance from a massive body.

Gravitational field strength
9.82 N/kg
Field strength g = G·M ÷ r² at the given distance from the source mass.
Free-fall acceleration
9.82 m/s²
Multiple of Earth g
1.0014 g

How it works

  1. 1Enter the source mass M in kilograms (scientific notation like 5.972e24 is accepted) and the distance r from its centre in metres.
  2. 2The calculator applies g = G·M ÷ r², where G = 6.674×10⁻¹¹ N·m²/kg², and returns the field strength in N/kg.
  3. 3The result shows g in N/kg, the identical free-fall acceleration in m/s², and the value as a multiple of Earth’s gravity (9.80665 m/s²).

Use cases

  • Comparing surface gravity on different planets from their mass and radius.
  • Studying how gravity weakens with altitude via the inverse-square falloff.
  • Finding the field strength at any orbital radius to check a satellite’s acceleration.

Frequently asked questions

What formula does this calculator use?

g = G·M ÷ r², where G ≈ 6.674×10⁻¹¹ N·m²/kg², M is the source mass in kg, and r is the distance from its centre in metres. For Earth (5.972×10²⁴ kg, 6.371×10⁶ m) it gives ≈ 9.82 N/kg.

Why does the result show both N/kg and m/s²?

They are dimensionally identical: 1 N/kg = 1 m/s². The N/kg view is the force per unit mass the field exerts; the m/s² view is the free-fall acceleration. Same number, different interpretation.

How does field strength change with distance?

It follows an inverse-square law — doubling the distance cuts g to a quarter. At Earth’s surface g ≈ 9.8 N/kg; at twice the radius ≈ 2.45 N/kg; at three times ≈ 1.09 N/kg.

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