Gravity Variation with Altitude Calculator

Track gravity loss as altitude steadily rises. See weight, ratios, and percent changes across worlds. Visual results support physics study, design checks, and planning.

Calculator Inputs

Enter a planet or custom body, then compare surface gravity with gravity at the selected altitude.

Example Data Table

Example values below use Earth and an 80 kg object to show how gravity and weight change as altitude increases.

Altitude (km) Gravity (m/s²) Weight for 80 kg (N) Percent Drop
0 9.806650 784.5320 0.0000%
10 9.775937 782.0750 0.3132%
100 9.505897 760.4717 3.0668%
400 8.682209 694.5768 11.4661%
1,000 7.326272 586.1018 25.2928%

Formula Used

The calculator uses the inverse-square gravity relation for altitude above a spherical body's surface:

g(h) = g₀ × [R / (R + h)]²

Where:

Weight is also computed from W = m × g.

Potential energy gain per kilogram uses ΔU/m = μ × (1/R − 1/(R+h)), where μ = g₀R².

The linear approximation shown in the chart is: g(h) ≈ g₀ × (1 − 2h/R). It works best at small altitudes.

How to Use This Calculator

  1. Select Earth, Moon, Mars, Jupiter, Saturn, or a custom body.
  2. Enter altitude and choose its unit.
  3. Add object mass if you want weight values in newtons.
  4. Adjust graph range multiplier and point count for smoother plotting.
  5. For a custom body, enter surface gravity and radius.
  6. Press Calculate Gravity Variation.
  7. Review the result panel above the form, then export CSV or PDF if needed.

FAQs

1. Why does gravity decrease with altitude?

Gravity weakens because the distance from the body's center increases. The inverse-square law means even moderate altitude changes reduce gravitational acceleration slightly.

2. Does an object's mass change with altitude?

No. Mass stays constant. Only weight changes because weight depends on local gravity. A body with the same mass weighs less where gravity is weaker.

3. Can I use this for the Moon or Mars?

Yes. The preset selector includes several worlds. Choose one, then enter your altitude. The calculator automatically applies that body's surface gravity and radius.

4. What is the normalized gravity ratio?

It is g(h) divided by surface gravity g₀. A value of 0.90 means gravity at altitude is 90% of the surface value.

5. When is the linear approximation reliable?

It works best when altitude is small compared with body radius. At higher altitudes, the full inverse-square relation is more accurate and should be trusted.

6. Does atmosphere affect the gravity value here?

No. This model focuses on gravitational change due to altitude only. It does not include drag, rotation, oblateness, or atmospheric density effects.

7. Why include escape velocity and potential energy?

They help show how altitude changes the wider orbital environment. These outputs are useful in physics study, mission planning, and engineering checks.

8. Can I enter feet or miles?

Yes. The calculator supports meters, kilometers, feet, and miles. It converts the selected unit internally before applying the gravity equations.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.