Schwarzschild Radius

The Schwarzschild Radius computes Radius (m) from 1 input: mass (kg). rs = 2GM/c².

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Schwarzschild Radius sits in that toolkit — it rs = 2GM/c². Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

M

Mass (kg)

Radius (m)

Output value

Radius (km)

Output value

1. 01Start by noting the input — Mass (kg): 1.989e+30.
2. 02Substitute these values into the formula: Radius (m) = 1.3348e-10 × e.M / 299792458² | Radius (km) = 1.3348e-10 × e.M / 299792458² / 1e3
3. 03Compute Radius (m): the calculator returns 2953.99.
4. 04Compute Radius (km): the calculator returns 2.95399.
5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.