What is the Schwarzschild radius and what does the calculator return?

The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole. It is the answer to the question: how small would you have to squeeze this mass before its gravity traps even light? The calculator takes a mass and returns that radius from R_s = 2GM/c². For example, one solar mass gives about 2954 metres, so if the Sun were crushed below a 3 km radius it would become a black hole.

How is the Schwarzschild radius formula derived?

Set the escape velocity at radius r equal to the speed of light c. Escape velocity is the square root of 2GM/r, so c² = 2GM/r, and solving for r gives r = 2GM/c². That r is the Schwarzschild radius. A full general-relativity derivation from the Schwarzschild metric lands on exactly the same expression, which is why the simple Newtonian shortcut happens to give the correct horizon radius.

How big is the Schwarzschild radius of the Earth and the Sun?

The Sun, at one solar mass (1.989e30 kg), has a Schwarzschild radius of about 2954 metres, roughly 3 km. The Earth, at 5.972e24 kg, has a Schwarzschild radius of about 8.87 millimetres, smaller than a marble. The numbers feel tiny because dividing by c² (about 9e16) shrinks everything enormously. Load the Earth or Sun preset to see both worked out step by step.

Does every object have a Schwarzschild radius?

Yes. Any mass has a Schwarzschild radius from R_s = 2GM/c², including a 70 kg person, who comes out near 1e-25 metres. That does not mean the object is a black hole. It only becomes one if its actual physical size is squeezed inside that radius. Normal objects are vastly larger than their Schwarzschild radius, so their event horizon is purely a what-if number rather than a real surface.

What are solar masses and why use them as a unit?

One solar mass, written M☉, is the mass of the Sun, about 1.989e30 kg. Astronomers measure stars and black holes in solar masses because writing 4.3 million solar masses is far easier than 8.5e36 kg. This calculator lets you type the mass in solar masses directly, so a value of 1 reproduces the Sun and a value of 4.297e6 reproduces Sagittarius A* at the centre of the Milky Way.

Is the Schwarzschild radius the same as the diameter of a black hole?

No, it is a radius, not a diameter. The full width of the event horizon is twice the Schwarzschild radius. So one solar mass has a horizon radius near 3 km but a horizon roughly 6 km across. The radius also assumes a non-rotating, uncharged black hole. A spinning black hole has a slightly different horizon described by the Kerr metric, but the Schwarzschild radius remains the standard reference figure.

Check a physics homework answer

Your astronomy problem set asks for the Schwarzschild radius of a three-solar-mass remnant. Type 3 in solar-mass mode, read the radius, and compare it against your hand calculation. The step-by-step breakdown shows R_s = 2GM/c² with the numbers substituted in, so if your answer is off you can see exactly which line diverged rather than re-deriving the whole thing.

Build intuition for how tiny event horizons are

Most people are surprised that the Earth's event horizon is under a centimetre and a person's is smaller than a proton. Punch in the Earth preset, then a 70 kg person, then the Sun, and watch the radius jump across thirty orders of magnitude. Seeing the raw numbers side by side makes the c² denominator concrete in a way a formula on paper does not.

Prep a classroom demo on black holes

Teaching a unit on general relativity, you want a live calculator on screen. Load the Sun preset to show the 3 km horizon, switch to Sagittarius A* to show the supermassive jump, and share the URL with students so they reopen the exact same setup at home. The light-second unit gives a feel for the scale of the largest horizons.

Inverse-solve a horizon back to a mass

You read that a particular black hole has an event horizon about 12 km across, and you want the mass behind it. Take half for the radius, switch the calculator to that radius, and read the mass it implies in solar masses. It turns a horizon size you found in an article into a number you can compare against catalogued objects.

Schwarzschild Radius Calculator — Event Horizon of a Black Hole

R_s = 2GM/c² — turn any mass into its black-hole event horizon, in metres, km or light-seconds, with presets and inverse solve — browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Mass M

Mass unit

Object presetRadius unitR_s = 2GM/c² · G = 6.674e-11 · c = 2.998e8 m/s

Schwarzschild radius2.954 km

This is the event horizon radius: compress the mass inside this radius and it becomes a black hole. Nothing, not even light, escapes from within it.

Formula steps

R_s = 2·G·M / c²
R_s = (2 × 6.674e-11 × 1.9890e+30) / (2.99792458e8)²
R_s = (2 × 6.674e-11 × 1.9890e+30) / 8.9876e+16
R_s = 2,954 m
R_s = 2.954 km

What this tool does

Free Schwarzschild radius calculator for the event horizon of a non-rotating black hole. Enter a mass in kilograms or in solar masses and the tool returns its Schwarzschild radius, the radius you would have to compress that whole mass inside for it to become a black hole. The formula is R_s = 2GM/c², where G is the gravitational constant and c is the speed of light. The Sun (one solar mass) collapses to about 3 km, the Earth to about 8.9 mm, and a 70 kg person to a radius far smaller than a proton. You can read the answer in metres, kilometres or light-seconds, switch the input between kg and solar masses, load presets for the Earth, the Sun and Sagittarius A* at the centre of the Milky Way, and inverse-solve a radius back to the mass that fits it. Every number is plain JavaScript in your browser, with a one-click copy and a shareable URL that reproduces your exact input. 100% client-side, no upload.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Schwarzschild Radius Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check a physics homework answer
Your astronomy problem set asks for the Schwarzschild radius of a three-solar-mass remnant. Type 3 in solar-mass mode, read the radius, and compare it against your hand calculation. The step-by-step breakdown shows R_s = 2GM/c² with the numbers substituted in, so if your answer is off you can see exactly which line diverged rather than re-deriving the whole thing.
Build intuition for how tiny event horizons are
Most people are surprised that the Earth's event horizon is under a centimetre and a person's is smaller than a proton. Punch in the Earth preset, then a 70 kg person, then the Sun, and watch the radius jump across thirty orders of magnitude. Seeing the raw numbers side by side makes the c² denominator concrete in a way a formula on paper does not.
Prep a classroom demo on black holes
Teaching a unit on general relativity, you want a live calculator on screen. Load the Sun preset to show the 3 km horizon, switch to Sagittarius A* to show the supermassive jump, and share the URL with students so they reopen the exact same setup at home. The light-second unit gives a feel for the scale of the largest horizons.
Inverse-solve a horizon back to a mass
You read that a particular black hole has an event horizon about 12 km across, and you want the mass behind it. Take half for the radius, switch the calculator to that radius, and read the mass it implies in solar masses. It turns a horizon size you found in an article into a number you can compare against catalogued objects.

Common pitfalls

Confusing the Schwarzschild radius with a diameter. The result is a radius; the horizon is twice as wide. Reporting one solar mass as a 3 km black hole is the radius, while the horizon itself spans about 6 km. Double the value before quoting a width.
Forgetting to match the mass unit to the input. Typing 1 while the calculator is in kilograms gives the horizon of a 1 kg object, not the Sun. Switch to solar-mass mode first, then type 1, or stay in kg and type 1.989e30.
Treating the radius as proof an object is a black hole. Every mass has a Schwarzschild radius, but an object is a black hole only if its real size is crushed inside that radius. The Earth has an 8.9 mm Schwarzschild radius yet is obviously not a black hole, because it is far larger than that.

Privacy

Every calculation, the R_s = 2GM/c² formula, the unit conversions and the inverse solve, is plain JavaScript that runs in your browser tab. The mass you enter and the radius you get never leave the page, and nothing is logged. The one caveat: the shareable URL encodes your mass and units in the query string, so a share link pasted into chat will record those values in the recipient server's access log. The inputs here are public physics quantities, so this is rarely a concern, but use the copy button if you would rather not put anything in a URL.

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Schwarzschild Radius Calculator — Event Horizon of a Black Hole

Formula steps

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Schwarzschild Radius Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check a physics homework answer

Build intuition for how tiny event horizons are

Prep a classroom demo on black holes

Inverse-solve a horizon back to a mass

Common pitfalls

Privacy

FAQ

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