G-force (n) is acceleration expressed in units of standard gravity: n = a/g₀ where g₀ = 9.80665 m/s². At 1g you feel normal weight standing still. At 0g you experience weightlessness (free fall). Fighter pilots can experience 5-9g during maneuvers. Car crashes can produce 10-50g. G-force = a/9.807 for any acceleration a in m/s².

Gravitational Force Calculator — Newton's Law, Planet Weight & G-Force

Physics · Gravity & Mechanics

Gravitational Force Calculator

Q: What is Newton's law of universal gravitation?

Newton's law of universal gravitation states that every mass attracts every other mass with a force F = G×m₁×m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses in kilograms, and r is the distance between their centers in meters. The gravitational force is always attractive, acts along the line connecting the centers, and obeys the inverse square law.

Q: What is the gravitational constant G?

The gravitational constant G = 6.67430×10⁻¹¹ N·m²/kg² is a fundamental physical constant that appears in Newton's law of universal gravitation F=Gm₁m₂/r² and Einstein's general relativity. It was first measured by Henry Cavendish in 1798 and is the same everywhere in the universe. G is the least precisely known fundamental constant — it is extremely small, reflecting that gravity is the weakest of the four fundamental forces.

Q: What two factors affect gravitational force?

Exactly two factors affect the gravitational force between two objects: (1) The masses of the two objects — gravitational force is directly proportional to each mass (double either mass → force doubles). (2) The distance between their centers — gravitational force is inversely proportional to the square of the distance (double the distance → force decreases by a factor of 4). No other factors affect gravitational force — not temperature, density, composition, or any other property.

Q: Why does weight change on different planets but mass does not?

Mass is the amount of matter in an object — it is constant everywhere in the universe (70 kg on Earth = 70 kg on Mars = 70 kg in space). Weight is the gravitational force on that mass: W = m × g, where g is the local surface gravity. Since different planets have different surface gravities (Mars g=3.721 m/s², Earth g=9.807 m/s², Moon g=1.62 m/s²), your weight changes but your mass never does.

Q: How much would I weigh on Mars?

On Mars you would weigh 37.9% of your Earth weight. Mars surface gravity is g=3.721 m/s² compared to Earth's 9.807 m/s². Formula: W_Mars = mass × 3.721. Example: 70 kg person weighs 686.5 N on Earth but only 260.5 N (58.6 lbf) on Mars. A 100 lb person would weigh about 37.9 lbs on Mars.

Q: How do you calculate impact force?

Impact force from a falling object: F = mv²/(2d), where m is mass, v is impact velocity (v=√(2gh) for fall from height h), and d is stopping distance. Example: 5 kg falling 10 m, stopping over 5 cm: v=√(2×9.807×10)=14.01 m/s, F=5×196.2/(2×0.05)=9,810 N. Shorter stopping distance = larger impact force — this is why crumple zones and helmets save lives.

Q: What is surface gravity?

Surface gravity is the gravitational acceleration at the surface of a planet, calculated by g = GM/r², where G = 6.674×10⁻¹¹ N·m²/kg², M is the planet mass, and r is the planet radius. Earth: g=9.807 m/s². Mars: g=3.721 m/s². Moon: g=1.62 m/s². Jupiter: g=24.79 m/s². Surface gravity is also called gravitational field strength and has units m/s² = N/kg.

Calculate the gravitational force between any two masses using Newton's Law of Universal Gravitation (F=Gm₁m₂/r²), find your weight on all planets and the Moon, determine surface gravity, and calculate g-force and impact force — with full step-by-step working throughout.

Gravitational Force Calculator — F=Gm₁m₂/r²

F = G × m₁ × m₂ / r² = ? N

Earth + Moon

Earth + Sun

Two 1kg balls, 1m

70kg + Earth (weight!)

Two 70kg people, 1m

Mass m₁:

Mass m₂:

Distance r (between centers):

Error

Newton's Law of Universal Gravitation — F=Gm₁m₂/r²

F = — N

Always Attractive — gravity never repels

Gravity Diagram — Bidirectional Attractive Force

Inverse Square Law — F ∝ 1/r² (two factors affect gravitational force)

—

At r/2 (4× force)

—

At r (original)

—

At 2r (¼ force)

Step-by-Step — Newton's Law of Universal Gravitation

—

Enter your mass or Earth weight to see how much you would weigh on every planet, the Moon, and the Sun. Your mass stays constant — only weight changes with planet gravity.

70 kg person

100 lb person

150 lb person

80 kg person

50 kg person

Your mass (or Earth weight):

Unit:

Error

Your Weight on Other Planets — W = m × g_planet

Mass: — kg

Mass is constant everywhere · Weight = m × g varies by planet

Planet Weight Bar Chart — Your Weight Across the Solar System

Body	g (m/s²)	Weight (N)	Weight (lbf)	vs Earth	Description

Steps — Weight on Other Planets

g = G × M / r² = ? m/s²

Mars

Earth

Moon

Jupiter

Sun

Venus

Quick select planet (auto-fills M and r):

Planet mass M (kg):

Planet radius r:

Radius unit:

Error

Surface Gravity (Gravitational Field Strength)

g = — m/s²

—

Step-by-Step — g=GM/r²

—

n = a / g₀ | g₀ = 9.80665 m/s²

Acceleration a (m/s²):

1g (normal)

5g (fighter jet)

10g (car crash)

0g (weightless)

Δv (km/h):

Δt (seconds):

Speed v (km/h):

Turn radius r (m):

Error

G-Force — Acceleration in Units of Gravity

n = — g

G-Force Gauge

Steps — G-Force Calculation

G-Force Reference Table

Situation	G-Force	Effect
Standing still	1 g	Normal
Sneeze	2.9 g	Brief, harmless
Roller coaster	3–5 g	Thrilling
Fighter jet turn	5–9 g	G-suit needed
Car crash (minor)	10–20 g	Injury risk
Ejector seat	14–16 g	Survivable
Fatal crash	>50 g	Usually fatal
Bullet fired	30,000 g	Instantaneous

F = mv²/(2d) | v = √(2gh)

5kg from 10m, 5cm stop

80kg from 2m, 5cm

1kg from 1m, 1cm

Mass m (kg):

Fall height h (m):

Stopping distance d (m):

Car 1500kg@60km/h, 0.5m

Person 80kg@30km/h, 10cm

Mass m (kg):

Velocity (km/h):

Stopping distance d (m):

Error

Impact Force — F = mv²/(2d)

F = — N

Steps — Impact Force Calculation

—

Newton's Law of Universal Gravitation — F = Gm₁m₂/r²

This gravitational force calculator uses Newton's Law of Universal Gravitation to compute the attractive force between any two masses. The fundamental formula F=Gm₁m₂/r² tells us that every object with mass attracts every other object with mass — from two hydrogen atoms to the Earth and Moon. Newton's Law of Universal Gravitation is one of the most powerful and universal equations in all of physics.

F = G × m₁ × m₂ / r² = 6.674×10⁻¹¹ × m₁ × m₂ / r² Newton's Law of Universal Gravitation — F=Gm₁m₂/r² — gravitational force in Newtons (N)

The gravitational constant G = 6.674×10⁻¹¹ N·m²/kg² is a fundamental constant — the same everywhere in the universe. Two key facts about gravitational force: (1) it is always attractive — gravity never repels, unlike electric and magnetic forces; (2) it obeys the inverse square law — doubling the distance decreases the gravitational force by a factor of 4. The gravitational force F=Gm₁m₂/r² acts equally on both objects (Newton's 3rd law).

Why G is so small: gravity is the weakest of the four fundamental forces. The gravitational force between two 1 kg balls at 1 m apart is only 6.674×10⁻¹¹ N — thousands of billions of times weaker than the electromagnetic force between two electrons. Yet gravity dominates the universe at large scales because it acts over infinite range and is always attractive (unlike charges which can cancel). The gravitational force from F=Gm₁m₂/r² between Earth (5.972×10²⁴ kg) and the Moon (7.342×10²² kg) reaches 1.978×10²⁰ N.

Mathematical equation for gravity: F = Gm₁m₂/r² where G=6.674×10⁻¹¹ N·m²/kg², masses in kg, distance in meters, force in Newtons. The force of attraction formula shows that two objects attract each other gravitationally with equal and opposite forces — Earth pulls the Moon and the Moon pulls Earth with the same gravitational force magnitude.

What Two Factors Affect Gravitational Force?

Exactly two factors affect gravitational force — no more, no less. This is one of the most commonly tested facts about Newton's Law of Universal Gravitation:

Factor 1: The masses of the two objects (m₁ and m₂). Gravitational force is directly proportional to each mass. Double m₁ → force doubles. Double both masses → force quadruples. Gravitational force and mass are directly proportional: F ∝ m₁ × m₂.
Factor 2: The distance between the centers of the two objects (r). Gravitational force is inversely proportional to the SQUARE of the distance. This is the factor that most students get wrong. Double r → force decreases by factor 4 (not 2). Triple r → force decreases by factor 9. The relationship between distance and gravity follows F ∝ 1/r².

No other factors affect the strength of gravitational force — not temperature, color, composition, density, or anything else. A steel sphere and a wooden sphere of the same mass feel identical gravitational attraction. To increase the amount of gravitational force between two objects: increase either mass, or decrease the distance between them. These are the only two ways to change the gravitational force between two objects.

Change	Effect on F=Gm₁m₂/r²	Reason
Double m₁	F × 2	F ∝ m₁
Double m₂	F × 2	F ∝ m₂
Double both masses	F × 4	F ∝ m₁m₂
Double distance r	F ÷ 4	F ∝ 1/r²
Triple distance r	F ÷ 9	F ∝ 1/r²
Half the distance	F × 4	F ∝ 1/r²

Weight — The Measure of Gravitational Force on an Object

Weight is gravitational force: W = mg. A measure of the force of gravity on an object, weight is what the gravitational force calculator computes when you enter your mass and the local surface gravity. Weight has units of Newtons (SI) or pound-force (lbf). The measure of the pull of gravity on an object is your weight — and it changes depending on which planet you stand on.

The critical distinction: mass (kg) is the amount of matter — it never changes. Weight (N or lbf) is the gravitational force on that mass — it changes with location. A 70 kg person has a mass of 70 kg everywhere in the universe. Their weight in Newtons: 686.5 N on Earth (9.807 m/s²), 260.5 N on Mars (3.721 m/s²), 113.4 N on the Moon (1.62 m/s²). In everyday language "weight" often means mass, but in physics: weight = force = gravitational force exerted on an object = F_g. 1 kg on Earth weighs 9.807 N = 2.205 lbf. Gravity in Newtons at Earth's surface: g = 9.807 N/kg.

Weight on Other Planets — Your Weight Across the Solar System

Your weight on other planets differs because each planet has a different surface gravity g = GM/r². The weight on other planets formula is: W_planet = m × g_planet. Your mass is constant; only gravity changes. This is the physical meaning of F=Gm₁m₂/r² applied at a planet's surface.

Weight on Mars: Mars surface gravity = 3.721 m/s² (38% of Earth). 70 kg → 260.5 N (58.6 lbf). How much would I weigh on Mars: multiply your Earth weight by 0.3795. A 100 lb person weighs 37.95 lbs on Mars.
Weight on Jupiter: Jupiter surface gravity = 24.79 m/s² (2.528× Earth). 70 kg → 1735 N (390 lbf). Jupiter's enormous gravity means you would feel very heavy — 2.5× your Earth weight. How much would a 100 lb person weigh on Jupiter: 252.8 lbs.
Weight on the Moon: Moon surface gravity = 1.62 m/s² (16.5% of Earth). Apollo astronauts bounced in their suits because they felt so light. 70 kg on Earth = 113.4 N on the Moon. Weight on Earth vs Moon: 6.05:1 ratio.
Which planet would you weigh the least on: Pluto — g=0.62 m/s², only 6.3% of Earth gravity. A 100 lb person would weigh just 6.3 lbs on Pluto.
How much would I weigh on the Sun: Sun surface gravity = 274 m/s² (27.94× Earth). A 70 kg person would weigh 19,180 N = 4,313 lbf. How much would a 100 lb person weigh on Venus: g_Venus=8.87 m/s², ratio=0.905, weight=90.5 lbs.
Weight on Neptune: g = 11.15 m/s² (1.137× Earth) — actually stronger than Earth despite being an ice giant.

Surface Gravity Formula — g = GM/r²

Surface gravity is derived from Newton's Law of Universal Gravitation. At the surface of a planet with mass M and radius r, a small mass m feels a gravitational force F = GMm/r². The gravitational acceleration (surface gravity) is g = F/m = GM/r². This is the gravitational field strength formula — units m/s² = N/kg.

g = G × M / r² = gravitational field strength (m/s² = N/kg) Surface gravity — the equation for gravitational field strength at planet radius r

Example 1 — Surface gravity of Mars from M and r

g = GM/r² = 6.674×10⁻¹¹ × 6.4171×10²³ / (3.3895×10⁶)²
= 4.280×10¹³ / 1.149×10¹³ = 3.725 m/s² (actual: 3.721 m/s²)
Relative to Earth: 3.721/9.807 = 0.3795 g

Example 2 — Saturn's surprising surface gravity

g = GM/r² = 6.674×10⁻¹¹ × 5.683×10²⁶ / (5.823×10⁷)² = 10.44 m/s²
Saturn is 95× Earth's mass but only 1.065g surface gravity — because Saturn is very large and very low density (density < water)

Example 3 — Custom planet: M=3×10²⁴ kg, r=5000 km

g = 6.674×10⁻¹¹ × 3×10²⁴ / (5×10⁶)² = 2.002×10¹⁴ / 2.5×10¹³ = 8.01 m/s²

G-Force — Acceleration Measured in Units of Gravity

G-force (n) is acceleration expressed in multiples of standard gravity: n = a/g₀ where g₀ = 9.80665 m/s². At 1g: normal standing. At 0g: weightlessness (free fall or orbit). Negative g: upside-down, blood rushes to head. The g force calculator computes this from acceleration, velocity change, or circular motion.

From acceleration: n = a/9.807. Example: a=50 m/s² → n=5.10g (fighter pilot maneuver zone)
From velocity change (crash): n = Δv/(g₀×Δt). Car at 60→0 km/h in 0.3s: a=16.67/0.3=55.6 m/s², n=5.66g
Centripetal: n = v²/(r×g₀). Racing car at 200 km/h around r=100m: n=(55.56²/100)/9.807=3.15g

Physical effects: at 4-5g, blood pools in legs, vision grays. Above 9g sustained without G-suit: loss of consciousness. Car crashes: 10-50g depending on speed and crumple. This g acceleration calculator helps understand acceleration in physically meaningful terms.

Impact Force — How Hard Does a Falling Object Hit?

Impact force depends on mass, fall height, and — critically — stopping distance. The shorter the stopping distance, the greater the impact force. This is why car crumple zones, helmets, airbags, and padded floors save lives: they increase stopping distance, reducing the peak impact force. The formula: F = mv²/(2d), where v = √(2gh) for a fall from height h.

F_impact = mv²/(2d) | v = √(2gh) | g-force = F/(mg) Impact force equation — m=mass, v=impact velocity, d=stopping distance

Example 1 — 5kg object falls 10m, stops over 5cm

v = √(2×9.807×10) = 14.007 m/s
F = 5×14.007²/(2×0.05) = 5×196.2/0.1 = 9,810 N
G-force: 9810/(5×9.807) = 200.1g!

Example 2 — 80kg person falls 2m, stops over 5cm

v = √(2×9.807×2) = 6.264 m/s
F = 80×39.24/(0.1) = 31,392 N = 7,057 lbf
G-force = 40.1g — severely injurious

Example 3 — Car 1500kg at 60km/h, crumple zone 0.5m

v = 60 km/h = 16.667 m/s
F = 1500×16.667²/(2×0.5) = 1500×277.8/1.0 = 416,700 N = 41.7 tonnes-force
G-force = 28.3g — why seatbelts are essential

Common Mistakes in Gravitational Force Calculations

Mistake 1 — Confusing mass (kg) and weight (N)

❌ Wrong: "I weigh 70 kg on Mars" — your mass is 70 kg on Mars, not your weight
✅ Correct: Mass = 70 kg everywhere. Weight on Mars = 70×3.721 = 260.5 N. Weight measures the gravitational force exerted on an object.

Mistake 2 — Forgetting to SQUARE the distance in F=Gm₁m₂/r²

❌ Wrong: F = G×m₁×m₂/r (dividing by r instead of r²)
✅ Correct: F = G×m₁×m₂/r² — the denominator is r SQUARED. This is the most common arithmetic error in Newton's law calculations.

Mistake 3 — Using diameter instead of radius (or center-to-center distance)

❌ Wrong: Using the surface-to-surface distance as r
✅ Correct: r is the distance between CENTERS of mass. For two touching spheres of radii r₁ and r₂: r = r₁ + r₂. For Earth-Moon: r is center-to-center = 3.844×10⁸ m.

Mistake 4 — Wrong value of G (sign of exponent)

❌ Wrong: G = 6.674×10¹¹ (positive exponent)
✅ Correct: G = 6.674×10⁻¹¹ N·m²/kg² (negative exponent). Getting this wrong gives an answer 10²² times too large.

Mistake 5 — Thinking gravity depends on composition or density

❌ Wrong: "A denser material has stronger gravitational pull"
✅ Correct: Gravitational force depends ONLY on mass and distance (the two factors that affect gravitational force). A steel sphere and a wooden sphere of identical mass exert exactly the same gravitational force. Density and composition are irrelevant to F=Gm₁m₂/r².

Worked Examples — 8 Complete Problems

1. Earth-Moon gravitational force

F = G×m₁×m₂/r² = 6.674×10⁻¹¹×5.972×10²⁴×7.342×10²²/(3.844×10⁸)²
= 6.674×10⁻¹¹×4.383×10⁴⁷/1.478×10¹⁷ = 1.978×10²⁰ N

2. Two 1kg balls at 1m — gravity is weak!

F = 6.674×10⁻¹¹×1×1/1² = 6.674×10⁻¹¹ N (67 picoNewtons)

3. 70kg person on Earth — their weight IS gravitational force

W = m×g = 70×9.807 = 686.5 N = 154.3 lbf

4. 70kg person on Mars — weight on Mars

W = 70×3.721 = 260.5 N = 58.6 lbf (38% of Earth weight)

5. Surface gravity of Mars from M and r

g = GM/r² = 6.674×10⁻¹¹×6.417×10²³/(3.390×10⁶)² = 3.721 m/s²

6. G-force: car crash 60→0 km/h in 0.3s

Δv = 60 km/h = 16.67 m/s; a = 16.67/0.3 = 55.56 m/s²
n = 55.56/9.807 = 5.67g (fighter pilot zone — dangerous!)

7. Impact force: 80kg person falls 2m, stops over 5cm

v = √(2×9.807×2) = 6.264 m/s; F = 80×39.24/0.1 = 31,392 N

8. 100 lb person on Venus (how much would a 100 lb person weigh on Venus?)

Mass = 100 lbf / 2.2046 = 45.36 kg
W_Venus = 45.36 × 8.87 = 402.3 N = 90.5 lbf (90.5% of Earth weight)

Frequently Asked Questions — Gravitational Force

What is Newton's law of universal gravitation?

Newton's Law of Universal Gravitation states that every mass attracts every other mass with a force F = G×m₁×m₂/r², where G=6.674×10⁻¹¹ N·m²/kg², m₁ and m₂ are masses in kg, and r is center-to-center distance in meters. The gravitational force is always attractive, obeys the inverse square law, and acts equally on both objects.

What is the gravitational constant G?

G = 6.67430×10⁻¹¹ N·m²/kg² is the universal gravitational constant. It appears in F=Gm₁m₂/r² and g=GM/r². First measured by Henry Cavendish in 1798, G is the same everywhere in the universe. It is extremely small, reflecting that gravity is the weakest fundamental force.

What two factors affect gravitational force?

Exactly two factors affect gravitational force: (1) The masses — F is directly proportional to each mass (double m₁ → force doubles). (2) The distance between centers — F is inversely proportional to r² (double r → force decreases by factor 4). Nothing else — not temperature, composition, or density — affects the gravitational force F=Gm₁m₂/r².

Why does weight change on different planets but mass does not?

Mass is the amount of matter — constant everywhere. Weight is the gravitational force on that mass: W=mg. Since g=GM/r² differs by planet (Earth: 9.807 m/s², Mars: 3.721 m/s², Moon: 1.62 m/s²), your weight changes but mass never does. A 70 kg person is always 70 kg but weighs 686.5N on Earth, 260.5N on Mars, 113.4N on the Moon.

How much would I weigh on Mars?

On Mars you weigh 37.95% of your Earth weight. Mars surface gravity: g=3.721 m/s². Multiply your mass (kg) by 3.721 to get Newtons. To convert from Earth weight in lbs: multiply by 0.3795. Example: 150 lbs on Earth → 56.9 lbs on Mars. 100 lbs → 37.95 lbs on Mars.

What is g-force?

G-force n = a/g₀ is acceleration expressed in multiples of standard gravity (g₀=9.80665 m/s²). At 1g you feel normal. At 0g you float (weightlessness). At 5g your vision grays. Fighter pilots sustain 5-9g with G-suits. Car crashes produce 10-50g. The g force calculator computes n from any acceleration.

How do you calculate impact force?

Impact force from a falling object: F=mv²/(2d) where v=√(2gh) is impact velocity and d is stopping distance. A 5kg mass falling 10m stopping over 5cm: v=14.01m/s, F=5×196.2/0.1=9,810N (200g!). Shorter stopping distance = much larger impact force — this is why helmets and crumple zones save lives.

What is surface gravity?

Surface gravity g=GM/r² is the gravitational acceleration at a planet's surface, derived from Newton's Law of Universal Gravitation. Units: m/s² = N/kg (gravitational field strength). Values: Earth 9.807, Moon 1.62, Mars 3.721, Jupiter 24.79, Sun 274.0 m/s². It determines your weight on that body: W=m×g.

Related Calculators

Key Formulas

F = Gm₁m₂/r²Newton's law — gravitational force

G = 6.674×10⁻¹¹ N·m²/kg²Gravitational constant

g = GM/r²Surface gravity / g field strength

W = m × gWeight = gravitational force

n = a/g₀G-force (g₀=9.807 m/s²)

F = mv²/(2d)Impact force

v = √(2gh)Impact velocity from height

Double r → F÷4 (inv sq law)Two factors affect gravitational force

Planet Gravity

☿ Mercury: g=3.70 m/s²

♀ Venus: g=8.87 m/s²

🌍 Earth: g=9.807 m/s²

🌙 Moon: g=1.62 m/s²

♂ Mars: g=3.721 m/s²

♃ Jupiter: g=24.79 m/s²

☀ Sun: g=274.0 m/s²

Related Tools

Planet Reference

Planet	g (m/s²)	g/g_E
☿ Mercury	3.70	0.378
♀ Venus	8.87	0.905
🌍 Earth	9.807	1.000
🌙 Moon	1.62	0.165
♂ Mars	3.721	0.379
♃ Jupiter	24.79	2.528
♄ Saturn	10.44	1.065
⛢ Uranus	8.69	0.886
♆ Neptune	11.15	1.137
♇ Pluto	0.62	0.063
☀ Sun	274.0	27.94

Reference Tables — Gravitational Physics

Table A — Planet Properties (hardcoded)

Planet	Mass (kg)	Radius (km)	g (m/s²)	g/g_Earth
☿ Mercury	3.301×10²³	2,440	3.70	0.378
♀ Venus	4.868×10²⁴	6,052	8.87	0.905
🌍 Earth	5.972×10²⁴	6,371	9.807	1.000
🌙 Moon	7.342×10²²	1,737	1.62	0.165
♂ Mars	6.417×10²³	3,390	3.721	0.379
♃ Jupiter	1.898×10²⁷	69,911	24.79	2.528
♄ Saturn	5.683×10²⁶	58,232	10.44	1.065
⛢ Uranus	8.681×10²⁵	25,362	8.69	0.886
♆ Neptune	1.024×10²⁶	24,622	11.15	1.137
♇ Pluto	1.303×10²²	1,188	0.62	0.063
☀ Sun	1.989×10³⁰	695,700	274.0	27.94

Table B — What Two Factors Affect Gravitational Force

Factor	Effect on F=Gm₁m₂/r²	Formula
Mass of objects	Double m₁ → F doubles	F ∝ m₁ × m₂
Distance between objects	Double r → F decreases by 4×	F ∝ 1/r²

Table C — Gravitational Constant G

Property	Value
Symbol	G
Value	6.67430×10⁻¹¹ N·m²/kg²
SI units	N·m²/kg²
First measured by	Henry Cavendish (1798)
Uncertainty	±0.00015×10⁻¹¹ (most uncertain fundamental constant)
Standard gravity g₀	9.80665 m/s² (exact SI)

Table D — Weight vs Mass vs G-Force

Term	Definition	Unit	Changes with location?
Mass	Amount of matter	kg	No — constant everywhere
Weight	Gravitational force on mass (W=mg)	N (or lbf)	Yes — varies by planet
G-force	Acceleration in units of g	dimensionless	Yes
g (surface gravity)	Gravitational field strength = GM/r²	m/s² = N/kg	Yes — by planet

Written by

Shahid Ali

Scientific Tools Developer & Research Analyst · SciSolveLab

🧬 Biology ⚗️ Chemistry 📐 Mathematics ⚡ Physics

100+ Calculators

142 Articles

Technical Researcher Scientific Tools

Shahid Ali is the creator and lead developer of SciSolveLab, a platform dedicated to making complex scientific and mathematical computations accessible. With a deep background in physics, thermodynamics, and wave mechanics, Shahid's work is driven by the belief that robust, accurate mathematical tools should be just a click away for students, engineers, and researchers.

Gravitational Force Calculator — Newton’s Law, Planet Weight & G-Force

Gravitational Force Calculator

Newton's Law of Universal Gravitation — F = Gm₁m₂/r²

What Two Factors Affect Gravitational Force?

Weight — The Measure of Gravitational Force on an Object

Weight on Other Planets — Your Weight Across the Solar System

Surface Gravity Formula — g = GM/r²

Example 1 — Surface gravity of Mars from M and r

Example 2 — Saturn's surprising surface gravity

Example 3 — Custom planet: M=3×10²⁴ kg, r=5000 km

G-Force — Acceleration Measured in Units of Gravity

Impact Force — How Hard Does a Falling Object Hit?

Example 1 — 5kg object falls 10m, stops over 5cm

Example 2 — 80kg person falls 2m, stops over 5cm

Example 3 — Car 1500kg at 60km/h, crumple zone 0.5m

Common Mistakes in Gravitational Force Calculations

Mistake 1 — Confusing mass (kg) and weight (N)

Mistake 2 — Forgetting to SQUARE the distance in F=Gm₁m₂/r²

Mistake 3 — Using diameter instead of radius (or center-to-center distance)

Mistake 4 — Wrong value of G (sign of exponent)

Mistake 5 — Thinking gravity depends on composition or density

Worked Examples — 8 Complete Problems

1. Earth-Moon gravitational force

2. Two 1kg balls at 1m — gravity is weak!

3. 70kg person on Earth — their weight IS gravitational force

4. 70kg person on Mars — weight on Mars

5. Surface gravity of Mars from M and r

6. G-force: car crash 60→0 km/h in 0.3s

7. Impact force: 80kg person falls 2m, stops over 5cm

8. 100 lb person on Venus (how much would a 100 lb person weigh on Venus?)

Frequently Asked Questions — Gravitational Force

Related Calculators

Shahid Ali

Pages

Newsletter

Gravitational Force Calculator — Newton’s Law, Planet Weight & G-Force

Gravitational Force Calculator

Newton's Law of Universal Gravitation — F = Gm₁m₂/r²

What Two Factors Affect Gravitational Force?

Weight — The Measure of Gravitational Force on an Object

Weight on Other Planets — Your Weight Across the Solar System

Surface Gravity Formula — g = GM/r²

Example 1 — Surface gravity of Mars from M and r

Example 2 — Saturn's surprising surface gravity

Example 3 — Custom planet: M=3×10²⁴ kg, r=5000 km

G-Force — Acceleration Measured in Units of Gravity

Impact Force — How Hard Does a Falling Object Hit?

Example 1 — 5kg object falls 10m, stops over 5cm

Example 2 — 80kg person falls 2m, stops over 5cm

Example 3 — Car 1500kg at 60km/h, crumple zone 0.5m

Common Mistakes in Gravitational Force Calculations

Mistake 1 — Confusing mass (kg) and weight (N)

Mistake 2 — Forgetting to SQUARE the distance in F=Gm₁m₂/r²

Mistake 3 — Using diameter instead of radius (or center-to-center distance)

Mistake 4 — Wrong value of G (sign of exponent)

Mistake 5 — Thinking gravity depends on composition or density

Worked Examples — 8 Complete Problems

1. Earth-Moon gravitational force

2. Two 1kg balls at 1m — gravity is weak!

3. 70kg person on Earth — their weight IS gravitational force

4. 70kg person on Mars — weight on Mars

5. Surface gravity of Mars from M and r

6. G-force: car crash 60→0 km/h in 0.3s

7. Impact force: 80kg person falls 2m, stops over 5cm

8. 100 lb person on Venus (how much would a 100 lb person weigh on Venus?)

Frequently Asked Questions — Gravitational Force

Related Calculators

Share This Tool

Shahid Ali

Pages

Newsletter