Black Hole Calculator

Compute Schwarzschild radius, Hawking temperature, tidal forces, event horizon area, and gravitational time dilation for any black hole mass. Based on Einstein's field equations and quantum gravity (Hawking radiation).

M☉ (Solar masses)

Physics of Black Holes: From Schwarzschild to Hawking

A black hole is a region of spacetime where gravity is so intense that nothing—not even light—can escape. The boundary is called the event horizon. This calculator uses general relativity and quantum field theory in curved spacetime to compute essential properties of non-rotating (Schwarzschild) black holes, which are the simplest and most studied type.

Schwarzschild radius: \( R_s = \frac{2GM}{c^2} \)   |   Hawking temperature: \( T_H = \frac{\hbar c^3}{8\pi G M k_B} \)
Time dilation: \( \frac{\Delta t'}{\Delta t} = \sqrt{1 - \frac{R_s}{r}} \)   |   Tidal acceleration: \( \Delta g = \frac{2GM}{r^3} \Delta r \)
Solar Mass
1 M☉ = 1.989 × 10³⁰ kg
Schwarzschild Radius
Rₛ = 2GM/c²
Hawking Radiation
T ∝ 1/M

? Key Parameters Explained

  • Schwarzschild radius (Rₛ): Radius of the event horizon. For a solar-mass black hole, Rₛ ≈ 2.95 km.
  • Hawking temperature (T_H): Quantum effect – black holes emit blackbody radiation. Stellar black holes have extremely low temperature (nanoKelvin), while micro black holes could be hot.
  • Time dilation factor: Clocks slow down near the horizon. At r = Rₛ, time stops (from distant view).
  • Tidal forces: Difference in gravitational pull across an object; causes spaghettification near stellar-mass holes.
  • Photon sphere: Radius at which light orbits the black hole (1.5 Rₛ).
  • Evaporation time: Time for a black hole to completely evaporate via Hawking radiation.

Astrophysical & Observational Evidence

Gravitational Waves (LIGO/Virgo)

Mergers of stellar-mass black holes produce gravitational waves. The observed chirp mass directly relates to the Schwarzschild radius and inspiral dynamics. Our calculator lets you estimate the final black hole's event horizon size after merger.

Event Horizon Telescope (EHT)

In 2019, EHT captured the first image of M87*'s shadow. The dark region corresponds to the photon sphere and event horizon. Using our calculator, input M87* mass (6.5e9 M☉) → Rₛ ≈ 19 billion km (≈ 130 AU).

Hawking Radiation & Black Hole Thermodynamics

Hawking's 1974 discovery united gravity and quantum mechanics. Though stellar black holes are extremely cold (nanoKelvin), primordial black holes of mass ~10¹² kg would have temperature ~10¹¹ K and emit gamma rays. Our calculator computes evaporation time – for a 1 M☉ black hole, t_evap >> age of universe.

Reference Table: Known Black Holes

Object Mass (M☉) Rₛ (km) T_H (K) Evaporation time (years)
GW190521 (merger remnant) ~142 420 4.3e-9 ~1.3e67
Sagittarius A* (Milky Way) 4.3e6 1.27e7 1.4e-14 ~1.3e87
M87* 6.5e9 1.92e10 9.4e-18 ~6.7e99
Primordial black hole (asteroid mass) ~10⁻¹⁶ ~3e-13 ~10¹¹ ~10⁶ years

Frequently Asked Questions

No known process can destroy a black hole; Hawking radiation only causes extremely slow evaporation over cosmological timescales.

Schwarzschild black holes are non‑rotating; Kerr black holes rotate and have an ergosphere. This calculator focuses on the Schwarzschild case (most common for introductory GR).

It is a theoretical prediction accepted by the physics community; direct detection is beyond current technology due to extremely low temperatures of astrophysical black holes.
References: Misner, Thorne, Wheeler "Gravitation" (1973); Hawking, S.W. (1974) "Black hole explosions?" Nature; LIGO Scientific Collaboration; EHT Collaboration 2019. Constants: G = 6.67430×10⁻¹¹ m³ kg⁻¹ s⁻², c = 299792458 m/s, ħ = 1.0545718×10⁻³⁴ J·s, k_B = 1.380649×10⁻²³ J/K.