Gravitational Field Strength Calculator
Calculate gravitational field strength g = G·M ÷ r² at any distance from a massive body.
How it works
- 1Enter the source mass M in kilograms (scientific notation like 5.972e24 is accepted) and the distance r from its centre in metres.
- 2The calculator applies g = G·M ÷ r², where G = 6.674×10⁻¹¹ N·m²/kg², and returns the field strength in N/kg.
- 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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