Gravity Calculator | Free Fall, Force & Escape
Calculate free fall height, time, and velocity. Compute gravitational force with Newton's law. Find surface gravity and escape velocity for any planet. NASA planet data included.
QUICK PRESETS
Enter any one value to solve for the other two.
| Body | g (m/s²) | vs Earth |
|---|---|---|
| Mercury | 3.70 | 0.377 g |
| Venus | 8.87 | 0.904 g |
| Earth | 9.81 | 1.000 g |
| Moon | 1.62 | 0.165 g |
| Mars | 3.72 | 0.379 g |
| Jupiter | 24.79 | 2.528 g |
| Saturn | 10.44 | 1.065 g |
| Uranus | 8.87 | 0.904 g |
| Neptune | 11.15 | 1.137 g |
| Pluto | 0.62 | 0.063 g |
| Sun | 274.00 | 27.940 g |
What Is the Gravity Calculator | Free Fall, Force & Escape?
This gravity calculator covers four modes: free-fall kinematics (solve for height, time, or velocity), Newton's gravitational force between two masses, surface gravity of any spherical body, and escape velocity. Uses the NIST CODATA 2018 value G = 6.674×10⁻¹¹ N·m²/kg² and standard gravity g = 9.80665 m/s².
- ▸Free Fall: Enter any one of height, time, or velocity, the calculator solves for the other two. Select surface gravity from any planet or enter a custom g.
- ▸Gravitational Force: Computes F = Gm₁m₂/r² for any two masses at any distance. Presets for Earth-Moon, Earth-Sun, and Earth-person.
- ▸Surface Gravity: Given a body's mass and radius, finds its surface g. Includes Earth, Moon, Mars, and Jupiter presets.
- ▸Escape Velocity: Computes vₑ = √(2GM/R), the speed needed to escape a planet's gravity from its surface.
- ▸Planet table: Shows NASA surface gravity for all 8 planets, Moon, Pluto, and Sun.
Formula
Free Fall
h = ½gt² v = gt t = √(2h/g)
g = 9.80665 m/s² on Earth (standard). Select any planet for its surface g.
Newton's Law of Gravitation
F = G × m₁ × m₂ / r²
G = 6.674×10⁻¹¹ N·m²/kg² (NIST CODATA 2018)
Surface Gravity
g = G × M / R²
Derives surface gravitational acceleration from mass M and radius R of a body.
Escape Velocity
vₑ = √(2GM/R)
Minimum speed to escape gravitational field from surface, ignores atmospheric drag.
How to Use
- 1
Select a mode
Choose Free Fall, Gravitational Force, Surface Gravity, or Escape Velocity.
- 2
Try a preset
Click presets like Drop 10 m, Empire State, Moon landing, or Mars mission to auto-fill values.
- 3
Select a planet (Free Fall)
Click any planet button to set that body's surface gravity, or enter a custom g value.
- 4
Choose your units
Select m, ft, or km for distances; kg or lb for masses using the inline dropdowns.
- 5
Enter your known value
In Free Fall, enter any one of height, time, or velocity. In force/gravity modes, enter mass and distance.
- 6
Press Calculate
Results appear instantly with all derived values including equivalent units.
- 7
Check the planet table
In Free Fall mode, the planet gravity reference table shows NASA g values for all solar system bodies.
- 8
Expand step-by-step
Click Step-by-step working to see every formula substitution with your values.
Example Calculation
Example 1 | Free fall from Empire State Building (443 m)
No air resistance assumed. Actual terminal velocity is ~53 m/s for a human.
Example 2 | Gravitational force, Earth on a 70 kg person
This equals 70 kg × 9.80 m/s² = 686 N, confirming the formula.
Example 3 | Escape velocity from Earth
Rockets must exceed this speed to escape Earth's gravity well into space.
Understanding Gravity | Free Fall, Force & Escape
Gravity in Physics
Gravity is the fundamental force attracting any two masses. Newton's law of universal gravitation quantifies this: F = Gm₁m₂/r². At planetary scale, this force determines orbits, tides, and surface weight. All calculations in this calculator run live in your browser using the NIST CODATA 2018 gravitational constant G = 6.674×10⁻¹¹ N·m²/kg².
Free Fall Assumptions
- ▸No air resistance, actual fall times are longer due to drag.
- ▸Uniform gravitational field, valid for heights small compared to Earth's radius.
- ▸Object released from rest (initial velocity = 0).
- ▸Standard Earth g = 9.80665 m/s², varies slightly with latitude and altitude.
Planet Surface Gravities (NASA)
Surface gravity varies enormously across the solar system. Jupiter's surface gravity is 2.53 times Earth's; the Moon's is only 0.165 g. The Sun's is 27.9 g. These values are computed from g = GM/R² using NASA mass and radius data.
Escape Velocity Notes
- ▸Earth: 11.19 km/s, rockets need this minimum speed ignoring air drag.
- ▸Moon: 2.38 km/s, much easier to escape, which is why the Moon has no atmosphere.
- ▸Jupiter: 59.5 km/s, strong gravity makes escape very difficult.
- ▸Sun: 617.5 km/s, nothing in the solar system escapes the Sun without additional energy.
Frequently Asked Questions
What is the value of g and why 9.80665 m/s²?
The standard acceleration of free fall is defined as exactly 9.80665 m/s² by the International Bureau of Weights and Measures. The actual value varies by location:
- • Equator: ≈9.78 m/s² (centrifugal effect reduces apparent gravity)
- • Poles: ≈9.83 m/s² (closer to Earth's center)
- • Standard: 9.80665 m/s² (used in all calculations here)
What is the gravitational constant G?
G is the universal gravitational constant, measured experimentally. This calculator uses the NIST CODATA 2018 value:
- • G = 6.67430×10⁻¹¹ N·m²/kg²
- • G is the least precisely known fundamental constant in physics
- • First measured by Henry Cavendish in 1798 using a torsion balance
How do I calculate fall time from height?
From the kinematic equation h = ½gt² (starting from rest, no air resistance):
- • Rearrange: t = √(2h / g)
- • Example: h = 100 m, g = 9.807 m/s² → t = √(200/9.807) ≈ 4.52 s
- • Enter height in the Free Fall tab and the calculator solves instantly.
Why does gravity vary on different planets?
Surface gravity depends on the planet's mass and radius: g = GM/R². A larger mass increases g, but a larger radius decreases it:
- • Jupiter has 318× Earth's mass but only 11× the radius → g ≈ 24.8 m/s²
- • Moon is 1/81 Earth's mass and 1/3.7 the radius → g ≈ 1.62 m/s²
What is escape velocity?
Escape velocity is the minimum speed needed to escape a body's gravitational field from its surface, ignoring air resistance:
- • vₑ = √(2GM/R)
- • Earth: 11.19 km/s | Moon: 2.38 km/s | Mars: 5.03 km/s
- • A body with vₑ > c (speed of light) is a black hole
Can I use pounds and feet in this calculator?
Yes. Each input has a unit selector:
- • Distance: m, ft, or km
- • Mass: kg or lb
- • The calculator converts to SI internally before computing, then displays results in your chosen units.
Does free-fall calculation account for air resistance?
No, these are idealized vacuum calculations. In practice, air resistance limits terminal velocity:
- • Human terminal velocity: ∼53 m/s (∼190 km/h)
- • Skydiver with parachute: ∼5–7 m/s
- • For precise engineering applications, use computational fluid dynamics models.
What is the difference between weight and gravitational force?
Weight is the gravitational force on a mass at a specific location:
- • Weight (N) = mass (kg) × local g (m/s²)
- • Your mass stays constant; your weight changes on different planets
- • F = G×M×m/R² = m×g (at surface)