Schwarzschild Radius Calculator

How it is calculated

The Schwarzschild radius of a non-rotating, uncharged mass is Rs = 2GM / c², where M is the mass in kilograms, G = 6.6743×10⁻¹¹ m³ kg⁻¹ s⁻² and c = 299,792,458 m/s. The mass can be entered in kilograms, solar masses (1.98892×10³⁰ kg) or Earth masses (5.972×10²⁴ kg); the tool converts it to kilograms first. The radius is shown in metres (two decimals) and in kilometres (four decimals). The radius grows in direct proportion to the mass, so ten times the mass gives ten times the radius. The mass must be above zero. An unrecognised unit is treated as solar masses.

Common mistakes

• Selecting the wrong unit, such as typing 1 for the mass but leaving kg selected. One kilogram has a radius of about 10⁻²⁷ m, which rounds to 0.00 m, while one solar mass gives nearly 3 km.
• Reading the radius as the size of an existing star. It is only the radius an object would have if squeezed into a black hole; the Sun is far larger than its own Schwarzschild radius.
• Confusing the radius with the diameter. The result is the radius; the horizon's diameter is twice as large.
• Using it for a spinning or charged black hole. This formula covers only the non-rotating, uncharged case.
• Expecting a result for Earth in kilometres. Earth gives about 0.01 m, which shows as 0.0000 km, so read the metre value.