Introduction
The Schwarzschild radius is the size an object would need to be compressed to in order to become a black hole. Named after physicist Karl Schwarzschild, who solved Einstein's field equations in 1916, this radius marks the event horizon — the boundary beyond which nothing, not even light, can escape a black hole's gravity. The formula is simple: Rs = 2GM/c², where G is the gravitational constant, M is the object's mass, and c is the speed of light.
This Schwarzschild Radius Calculator lets you find the event horizon size for any mass, from a tiny electron to the largest supermassive black holes in the universe. Enter a mass and the tool instantly computes the Schwarzschild radius in multiple units, along with key physics properties like Hawking temperature, surface gravity, photon sphere radius, tidal force, and average density. You can also work in reverse — enter a radius and find out how much mass would need to be packed inside it to form a black hole.
Use the built-in presets to explore real objects like Earth, the Sun, Sagittarius A* (the black hole at the center of our galaxy), or TON 618 (one of the most massive black holes ever found). The comparison library shows how your result stacks up against known black holes, making it easy to understand the scale of these extreme objects.
How to Use Our Schwarzschild Radius Calculator
Enter the mass of any object or a known Schwarzschild radius, and this calculator will compute the event horizon size, Hawking temperature, surface gravity, and other key black hole properties.
Calculate from Mass or Radius: Use the tabs at the top to choose your input method. Select "Calculate from Mass" if you know the object's mass, or "Calculate from Radius" if you already have a Schwarzschild radius and want to find the required mass.
Mass: Type in the mass of the object you want to analyze. You can enter plain numbers or use scientific notation by clicking the "×10ⁿ" button. For example, type "5.972e24" for Earth's mass in kilograms. If you need help formatting large or small numbers, our Scientific Notation Calculator can assist.
Unit: Pick the mass unit that matches your input. Choose from kilograms, metric tons, pounds, Earth masses, Jupiter masses, or solar masses. The default is set to solar masses, which is the most common unit for black hole calculations.
Decimal Places: Set how many decimal places you want in your results. You can choose anywhere from 0 to 10 for more or less detail.
Mass Scale Explorer: Drag the slider left or right to quickly explore how the Schwarzschild radius changes across a huge range of masses, from subatomic particles all the way up to supermassive objects.
Preset Objects: Click any preset button — Electron, Earth, Jupiter, Sun, Betelgeuse, Sagittarius A*, or TON 618 — to instantly load a well-known object's mass and see its Schwarzschild radius without typing anything.
Schwarzschild Radius (Radius Tab): If you switch to the "Calculate from Radius" tab, enter a known Schwarzschild radius value and select the matching unit — meters, kilometers, miles, astronomical units, or light-years. The calculator will then determine the mass needed to produce that event horizon.
Calculate / Reset: Press the "Calculate" button to run the computation. Your results will appear below, including the Schwarzschild radius in multiple units, a visual size comparison, extended physics properties like Hawking temperature, photon sphere radius, average density, tidal force, black hole type classification, and a comparison against famous known black holes. Press "Reset" to clear all inputs and start over.
What Is the Schwarzschild Radius?
The Schwarzschild radius is the size an object would need to be compressed to in order to become a black hole. Named after German physicist Karl Schwarzschild, who found this solution to Einstein's field equations in 1916, it defines the event horizon — the boundary around a black hole beyond which nothing, not even light, can escape. If you squeezed the entire Earth down to roughly the size of a marble (about 8.87 millimeters), it would become a black hole. That marble-sized boundary would be Earth's Schwarzschild radius.
The Formula: Rs = 2GM/c²
The calculation is straightforward. The Schwarzschild radius (Rs) equals two times the gravitational constant (G) times the object's mass (M), divided by the speed of light squared (c²). The gravitational constant G is 6.674 × 10⁻¹¹ m³/kg·s², and the speed of light c is about 299,792,458 meters per second. Because c² is such a huge number in the denominator, you need an enormous amount of mass to get even a small Schwarzschild radius. For example, our Sun — which contains 99.86% of our solar system's mass — has a Schwarzschild radius of only about 2.95 kilometers. This relationship between mass and energy is deeply connected to Einstein's famous equation explored in our E = mc² Calculator.
Why Does the Schwarzschild Radius Matter?
This concept is central to our understanding of general relativity and the life cycle of massive stars. When a star with more than about three times the Sun's mass runs out of fuel and collapses, no known force can stop it from shrinking past its own Schwarzschild radius. At that point, a stellar-mass black hole is born. The Gravitational Force Calculator can help you explore how gravity behaves between massive objects, but at the Schwarzschild radius, Newtonian gravity breaks down entirely and general relativity takes over. The Schwarzschild radius also helps astronomers classify black holes by size:
- Stellar-mass black holes — roughly 3 to 100 solar masses, with Schwarzschild radii from about 9 to 300 kilometers.
- Intermediate-mass black holes — hundreds to hundreds of thousands of solar masses, still being studied and confirmed.
- Supermassive black holes — millions to billions of solar masses, found at the centers of most galaxies. Sagittarius A*, the black hole at our galaxy's center, has a Schwarzschild radius of about 12 million kilometers.
- Ultramassive black holes — exceeding 10 billion solar masses. TON 618, one of the largest known, has a Schwarzschild radius larger than our entire solar system.
Related Physics Properties
Knowing the Schwarzschild radius lets you figure out several other important properties of a black hole. The photon sphere sits at 1.5 times the Schwarzschild radius — this is where light can orbit the black hole in an unstable circle. Hawking temperature, predicted by Stephen Hawking in 1974, describes the faint thermal radiation a black hole emits due to quantum effects near the event horizon. Smaller black holes are actually hotter; a black hole with the mass of the Sun would have a temperature near absolute zero, while a tiny primordial black hole could glow white-hot. This thermal radiation is closely related to the concept of half-life and radioactive decay, as black holes slowly evaporate over immense timescales. Tidal forces — the stretching effect sometimes called "spaghettification" — are stronger for smaller black holes because the curvature of space changes more sharply over short distances. To understand the basics of how objects respond to forces, you can explore our Force Calculator and Acceleration Calculator.
The surface gravity at the event horizon also relates to concepts you can explore with our Free Fall Calculator and G Force Calculator, though at a black hole's event horizon, these values reach extremes that defy everyday intuition. The Kinetic Energy Calculator and Potential Energy Calculator can help you understand the energy relationships that govern objects approaching such intense gravitational fields.
An Interesting Density Paradox
One surprising fact: supermassive black holes can have an average density lower than water. Because the Schwarzschild radius grows linearly with mass while volume grows as the cube of the radius, the average density inside the event horizon actually decreases as mass increases. A black hole with about 400 million solar masses would have an average density of roughly 1 kg/m³ — close to the density of air. This counterintuitive scaling is a great exercise in understanding how ratios work, something you can explore further with our Ratio Calculator. This means that if you were falling into a sufficiently large black hole, you might cross the event horizon without feeling anything unusual at first. There would be no wall, no surface, and no immediate sign that you had passed the point of no return.