Convert Gram-centimeters squared to Kilogram-meters squared
Instantly convert Gram-centimeters squared (g·cm²) to Kilogram-meters squared (kg·m²) with our free online calculator.
Formula: g·cm² to kg·m² — multiply by 1.0000e-7
Reference Table
| Gram-centimeters squared (g·cm²) | Kilogram-meters squared (kg·m²) |
|---|---|
| 1 | 1.000000e-7 |
| 5 | 5.000000e-7 |
| 10 | 0.000001 |
| 25 | 0.0000025 |
| 50 | 0.000005 |
| 100 | 0.00001 |
How to Convert Gram-centimeters squared to Kilogram-meters squared
Formula
To convert Gram-centimeters squared (g·cm²) to Kilogram-meters squared (kg·m²): multiply by 1.0000e-7
Step-by-Step
- Start with your value in Gram-centimeters squared (g·cm²).
- Multiply by 1.0000e-7 to perform the conversion.
- The result is your value expressed in Kilogram-meters squared (kg·m²).
Conversion Factor
1 g·cm² = 1.000000e-7 kg·m²
Reverse Factor
1 kg·m² = 10000000 g·cm²
Worked Example
Convert 25 Gram-centimeters squared to Kilogram-meters squared: 25 g·cm² = 0.0000025 kg·m²
About Gram-centimeter squared (g·cm²)
A CGS mass-moment-of-inertia unit equal to exactly 10⁻⁷ kg·m² = 0.1 mg·m². Used for very small precision components where SI units would produce many leading zeros: balance-wheel and escapement inertia in mechanical wristwatch movements (a typical Swiss-made automatic balance wheel has rotor inertia ~10⁻² g·cm²; this drives the resonant frequency that sets watch accuracy), instrument-grade gyroscope rotors (mechanical heading reference gyros and rate-integrating gyros in aerospace inertial-navigation systems before the MEMS transition), precision indexing wheels in optical encoders (Heidenhain, Renishaw encoder discs), MEMS resonator inertia in vibratory gyroscopes per IEEE 1431 silicon-resonator characterization, and historical-era optical precision instruments from European manufacturers (Zeiss, Leica, Carl Zeiss Jena pre-1970s) which still appear in vintage equipment overhaul references. Convert g·cm² to kg·m² by dividing by 10⁷; to lb·in² by dividing by 2,926.
About Kilogram-meter squared (kg·m²)
The SI unit of mass moment of inertia (ISO 80000-4 §4-12) — the rotational analog of mass, measuring a rigid body's resistance to angular acceleration about a specified axis (τ = I·α, the rotational form of Newton's second law). kg·m² is the universal working unit in rotational dynamics, flywheel-energy-storage design, gyroscope analysis, spacecraft attitude-control system (ACS) design, automotive driveline modeling (engine + clutch + transmission + driveshafts inertias propagated through gear ratios), and CAD/CAE mass-properties output (Autodesk Inventor, SolidWorks, CATIA, NX all compute Ixx/Iyy/Izz and the off-diagonal cross-products in kg·m²). Reference values: a typical 1-meter-radius solid steel cylinder of 100 kg ≈ 50 kg·m²; a figure skater's body mass moment of inertia changes from ~8 kg·m² (arms extended) to ~2 kg·m² (arms tucked tight) demonstrating angular-momentum conservation as spin rate increases ~4× when tucked; the International Space Station has ~10⁸ kg·m² principal-axis inertia. Convert kg·m² to lb·ft² by multiplying by 23.730; to slug·ft² by multiplying by 0.7376.
Quick Facts
- 1 Gram-centimeter squared equals 1.000000e-7 Kilogram-meters squared
- 1 Kilogram-meter squared equals 10000000 Gram-centimeters squared
- Gram-centimeter squared is a unit of mass moment of inertia
- Kilogram-meter squared is a unit of mass moment of inertia
- This conversion is commonly used in rotational dynamics, flywheel design, and robotics
- The Gram-centimeter squared belongs to the metric system
Common Gram-centimeter squared to Kilogram-meter squared Conversions
| Gram-centimeters squared (g·cm²) | Kilogram-meters squared (kg·m²) |
|---|---|
| 0.01 | 1.000000e-9 |
| 0.1 | 1.000000e-8 |
| 0.25 | 2.500000e-8 |
| 0.5 | 5.000000e-8 |
| 1 | 1.000000e-7 |
| 2 | 2.000000e-7 |
| 3 | 3.000000e-7 |
| 5 | 5.000000e-7 |
| 10 | 0.000001 |
| 15 | 0.0000015 |
| 20 | 0.000002 |
| 25 | 0.0000025 |
| 50 | 0.000005 |
| 75 | 0.0000075 |
| 100 | 0.00001 |
| 250 | 0.000025 |
| 500 | 0.00005 |
| 1000 | 0.0001 |
| 5000 | 0.0005 |
| 10000 | 0.001 |
Understanding Gram-centimeters squared
The Gram-centimeter squared (symbol: g·cm²) is a unit of mass moment of inertia. A CGS mass-moment-of-inertia unit equal to exactly 10⁻⁷ kg·m² = 0.1 mg·m². Used for very small precision components where SI units would produce many leading zeros: balance-wheel and escapement inertia in mechanical wristwatch movements (a typical Swiss-made automatic balance wheel has rotor inertia ~10⁻² g·cm²; this drives the resonant frequency that sets watch accuracy), instrument-grade gyroscope rotors (mechanical heading reference gyros and rate-integrating gyros in aerospace inertial-navigation systems before the MEMS transition), precision indexing wheels in optical encoders (Heidenhain, Renishaw encoder discs), MEMS resonator inertia in vibratory gyroscopes per IEEE 1431 silicon-resonator characterization, and historical-era optical precision instruments from European manufacturers (Zeiss, Leica, Carl Zeiss Jena pre-1970s) which still appear in vintage equipment overhaul references. Convert g·cm² to kg·m² by dividing by 10⁷; to lb·in² by dividing by 2,926.
It belongs to the metric measurement system.
Gram-centimeters squared are commonly used in rotational dynamics, flywheel design, and robotics.
Understanding Kilogram-meters squared
The Kilogram-meter squared (symbol: kg·m²) is a unit of mass moment of inertia. The SI unit of mass moment of inertia (ISO 80000-4 §4-12) — the rotational analog of mass, measuring a rigid body's resistance to angular acceleration about a specified axis (τ = I·α, the rotational form of Newton's second law). kg·m² is the universal working unit in rotational dynamics, flywheel-energy-storage design, gyroscope analysis, spacecraft attitude-control system (ACS) design, automotive driveline modeling (engine + clutch + transmission + driveshafts inertias propagated through gear ratios), and CAD/CAE mass-properties output (Autodesk Inventor, SolidWorks, CATIA, NX all compute Ixx/Iyy/Izz and the off-diagonal cross-products in kg·m²). Reference values: a typical 1-meter-radius solid steel cylinder of 100 kg ≈ 50 kg·m²; a figure skater's body mass moment of inertia changes from ~8 kg·m² (arms extended) to ~2 kg·m² (arms tucked tight) demonstrating angular-momentum conservation as spin rate increases ~4× when tucked; the International Space Station has ~10⁸ kg·m² principal-axis inertia. Convert kg·m² to lb·ft² by multiplying by 23.730; to slug·ft² by multiplying by 0.7376.
It belongs to the metric measurement system.
Kilogram-meters squared are commonly used in rotational dynamics, flywheel design, and robotics.
Why Convert Gram-centimeters squared to Kilogram-meters squared?
Converting between Gram-centimeters squared and Kilogram-meters squared is a frequent requirement for engineers, scientists, and students working with mass moment of inertia values. Different industries and regions favour different unit systems, so having a dependable conversion tool saves time and prevents errors in technical calculations. Whether you are verifying a specification sheet, cross-checking simulation results, or preparing a report for an international audience, accurate mass moment of inertia conversion is essential.
Frequently Asked Questions
How do I convert Gram-centimeters squared to Kilogram-meters squared?
A CGS mass-moment-of-inertia unit equal to exactly 10⁻⁷ kg·m² = 0. To convert Gram-centimeters squared to Kilogram-meters squared, multiply by 1.0000e-7. For example, 25 g·cm² equals 0.0000025 kg·m².
How many Kilogram-meters squared are in 1 Gram-centimeter squared?
There are 1.000000e-7 Kilogram-meters squared in 1 Gram-centimeter squared.
How many Gram-centimeters squared are in 1 Kilogram-meter squared?
There are 10000000 Gram-centimeters squared in 1 Kilogram-meter squared.
What is the formula for Gram-centimeter squared to Kilogram-meter squared conversion?
The formula is: multiply by 1.0000e-7. This means 1 g·cm² = 1.000000e-7 kg·m².
Is a Gram-centimeter squared bigger than a Kilogram-meter squared?
Yes. One Gram-centimeter squared is larger than one Kilogram-meter squared because 1 g·cm² equals 1.000000e-7 kg·m², which is less than 1.
When do you need to convert between Gram-centimeters squared and Kilogram-meters squared?
The SI unit of mass moment of inertia (ISO 80000-4 §4-12) — the rotational analog of mass, measuring a rigid body's resistance to angular acceleration about a specified axis (τ = I·α, the rotational form of Newton's seco... Gram-centimeter squared and Kilogram-meter squared are both mass moment units, so conversion comes up whenever one source of information uses one unit and another uses the other — a classic cross-reference challenge in engineering, trade, travel, and everyday life.