Unit converter with dimensional analysis
See each base unit change, one at a time.
Unit converter
newton = dyne
Step by step
- The dimension of forceForce has the dimensions [M L T⁻²]. Only the powers of M, L and T matter for the conversion.
- The conversion ruleA quantity with dimensions [Ma Lb Tc] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [L₁/L₂] [T₁/T₂]⁻².
- The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). L: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
- Put the numbers inn₂ = 1 [1 kg / 1 g] [1 m / 1 cm] [1 s / 1 s]⁻²
- Work out each bracket[M₁/M₂] = 1000; [L₁/L₂] = 100; [T₁/T₂]⁻² = 1⁻² = 1
- Multiplyn₂ = 1 × 1000 × 100 × 1 = 100,000
- The answer1 newton = 100,000 dyne
Common conversions
- Newton to dyne
- Dyne to newton
- Joule to erg
- Erg to joule
- Watt to erg per second
- Pascal to dyne per square centimetre
- Gravitational constant G, SI to CGS
- Density, kg per cubic metre to g per cubic centimetre
- Momentum, SI to CGS
- Angular momentum, SI to CGS
- Surface tension, newton per metre to dyne per centimetre
- Viscosity, pascal second to poise
- Kinematic viscosity, square metre per second to stokes
- Acceleration, metre per second squared to gal
- Newton to poundal
- Joule to foot-poundal
- Pascal to poundal per square foot
- Density, kg per cubic metre to pounds per cubic foot
Need the dimensions first? Look up any quantity in the dimensional formula tool.
Converting units with dimensions
How does dimensional analysis convert units?
A quantity with dimensions [Mᵃ Lᵇ Tᶜ] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in a new system, where M₁ and M₂ are the sizes of the mass unit in the two systems, and likewise for length and time.
Why is 1 newton equal to 100,000 dyne?
Force is [M L T⁻²]. A kilogram is 1000 grams and a metre is 100 centimetres, and the second is the same in both systems, so 1000 × 100 × 1 = 100,000.
Which systems can I use?
SI (kg, m, s), CGS (g, cm, s) and FPS (lb, ft, s), or a custom system where you give the size of each base unit in SI. Any quantity built from mass, length and time can be converted.
Why can I not convert current or temperature?
This converter changes the base units of mass, length and time. Quantities that also involve current, temperature, amount of substance or luminous intensity need a factor for those base units too.