g Constant in Physics: Meaning & Value

This page explains the gravitational constant g, the acceleration due to Earth’s gravity. You enter a height or simply want to know the standard value; the calculator below gives the acceleration at sea level and shows how it changes with altitude. You get the familiar 9.81 m/s² and a clear breakdown of the formula.

Formula

The standard formula for gravitational acceleration at a distance r from Earth’s center is:

g = G * M / r²

• G = gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg²
• M = mass of Earth, 5.972 × 10²⁴ kg
• r = distance from Earth’s center (meters) = Earth’s radius + height above sea level

At sea level, r = 6,371,000 m, so g = 9.80665 m/s². The calculator uses this value and adjusts it for altitude using the inverse-square law.

Worked Example

Using the defaults (height = 0 m):

1. r = 6,371,000 + 0 = 6,371,000 m
2. g = 9.80665 × (6,371,000 / 6,371,000)² = 9.80665 × 1 = 9.80665 m/s²

The calculator rounds to 9.807 m/s², which is the standard value used in physics problems.

What Exactly Is the g Constant?

In physics, g is the acceleration due to gravity at Earth’s surface. It is not a universal constant like G; it varies slightly with location, altitude, and latitude. The standard value is defined as 9.80665 m/s², adopted by international agreement for weights and measures.

It is also called “standard gravity” or “standard acceleration of free fall.” In everyday usage, people often say “g-force” or “gravity constant,” but technically those are different concepts.

Why Is g 9.81 and Not 9.8 or 10?

The value comes from Earth’s mass and radius. If Earth were denser or larger, g would be different. The 9.80665 value is an average at sea level; actual measurements range from about 9.78 at the equator to 9.83 at the poles because Earth is not a perfect sphere and rotates.

In many physics classes, you round to 9.8 or even 10 for quick mental math, but for precise work, use 9.80665.

How to Use the g Constant in Calculations

You use g whenever you need the force of gravity on a mass:

• Weight: F = m × g (e.g., a 10 kg object weighs 98.07 N)
• Free fall: d = ½ g t² (e.g., after 2 seconds, distance = 19.6 m)
• Potential energy: PE = m × g × h
• Pendulum period: T = 2π √(L/g)

Always use consistent units: meters, kilograms, seconds. If you use feet, g = 32.174 ft/s².

Common Misconceptions and Mistakes

A frequent error is confusing g (acceleration) with G (gravitational constant). G is universal and tiny; g is local and depends on the planet. Another mistake is using g = 9.8 for altitude calculations when the height is significant (e.g., satellites). At 100 km altitude, g drops to about 9.5 m/s².

Also, g is not a force; it is an acceleration. Weight is the force (mass × g). On the Moon, g ≈ 1.62 m/s², so a 10 kg object weighs 16.2 N there, not 98 N.

Limits of the Simple Formula

The inverse-square formula assumes Earth is a uniform sphere, which it is not. Real g varies with local geology (dense rock vs. water), latitude, and altitude. The standard 9.80665 is a reference value, not a universal measurement. For engineering, use local gravity values from geodetic surveys.

For most physics homework and everyday calculations, 9.81 m/s² is accurate enough. For high-precision work, use the International Gravity Formula that accounts for latitude and altitude.

Frequently Asked Questions

Is g the same everywhere on Earth?

No. It varies slightly with latitude (centrifugal force and Earth’s bulge) and altitude. The range is about 9.78 to 9.83 m/s². The standard 9.80665 is an average.

What is the difference between g and G?

g is the acceleration due to gravity at a specific location (m/s²). G is the universal gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²) that appears in Newton’s law of gravitation. They are not interchangeable.

Why do some textbooks use 9.8 and others 10?

It’s a rounding choice. 9.8 is closer to the actual value; 10 is used for rough mental calculations. For exams, use the value given in the problem or 9.81 unless told otherwise.

Does g change with height?

Yes. The formula g = G·M/r² shows that as r increases (higher altitude), g decreases. The calculator above shows this effect. For a 10 km airplane flight, g drops by about 0.3%.

How do I convert g to pounds-force?

In US customary units, g = 32.174 ft/s². To get weight in pounds-force, multiply mass in slugs by g, or use the fact that 1 kg weighs 2.20462 lbf at standard gravity.

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in h | Height above sea level | m | 0 | 0
out g | Gravitational acceleration | m/s² | 9.80665 * (6371000 / (6371000 + h))^2 | 3