Schwarzschild radius

This calculator uses the Schwarzschild model for an uncharged, nonrotating black hole. Enter a positive mass and calculate. The main result is the horizon's areal radius rₛ = 2GM/c²: its area is A = 4πrₛ². It is not a visual shadow diameter or an ordinary proper distance from a material center. No spin, electric charge or lensing model is included.

Mass units: kg, nominal solar masses M☉ and nominal Earth masses M⊕ are available. The conversion factors use the IAU 2015 nominal parameters (GM)☉ = 1.3271244 × 10²⁰ m³/s² and (GM)⊕ = 3.986004 × 10¹⁴ m³/s², divided by G. These are declared conversion conventions, not exact current measurements of the Sun or Earth. Changing units preserves the mass and displays the converted value with enough digits to retain the numerical value. An invalid mass must be corrected before changing units. Calculation uses the displayed input. Examples are mass scales, not claims of current precise measurements of individual objects.

Details: the comparison density is ρ = M/(4πrₛ³/3). This Euclidean volume comparison is not a local density inside the horizon. The semiclassical Hawking temperature is T_H = ℏc³/(8πGMk_B), and the Bekenstein–Hawking entropy is S = k_BAc³/(4ℏG), in J/K.

Approximate power and lifetime: treating the horizon area as a photon blackbody at T_H gives L = ℏc⁶/(15360πG²M²). Integrating dM/dt = −L/c² gives τ = 5120πG²M³/(ℏc⁴). These estimates assume an empty environment at 0 K, no accretion, no greybody correction and no additional emitted particle species. They are not realistic present-day lifetimes in an ambient radiation bath. Near or below the Planck mass, and during the final evaporation stage, semiclassical formulas are not reliable physical predictions. The calculator can still evaluate formal values when they remain numerically representable.

Constants and limits: G = 6.67430 × 10⁻¹¹ m³/(kg·s²) is the CODATA 2022 measured value and has uncertainty. The SI values c = 299792458 m/s, h = 6.62607015 × 10⁻³⁴ J·s and k_B = 1.380649 × 10⁻²³ J/K are exact; ℏ = h/(2π). A year (a) means a Julian year of 31557600 s. Display rounding is not an uncertainty estimate. There is no additional chosen mass maximum: all results and displayed unit conversions must be finite, positive normal binary64 values (at least 2⁻¹⁰²²). An out-of-range result produces an error instead of zero, infinity or a partial result. This is a numerical limit, not a physical mass bound.

Editing a mass, unit or example removes the result. Reset keeps the inputs; valid inputs are retained across navigation, and returning does not calculate automatically.

Sources: NIST, CODATA 2022 constants, pp. 1 and 6; IAU 2015 Resolution B3, recommendations 1–5, pp. 2–3; University of Zurich, PHY529 General Relativity III, pp. 6, 35 and 39–40, equations 6.17–6.24.