Event Horizon Radius Calculator
Calculate the Schwarzschild Radius (Event Horizon) of a Black Hole
The Event Horizon Radius (Schwarzschild radius) is:
Event Horizon Radius Calculator is a precise scientific tool that calculates the Schwarzschild radius — the radius of the event horizon of a non-rotating black hole — using Einstein’s general theory of relativity. Also known as the event horizon radius, this is the boundary beyond which nothing, not even light, can escape the gravitational pull of a black hole.
What is the Event Horizon Radius?
The event horizon radius, formally called the Schwarzschild radius (named after German physicist Karl Schwarzschild who derived it in 1916), defines the size of a black hole. Any object with mass compressed within its own Schwarzschild radius becomes a black hole.
The formula, derived directly from Einstein’s field equations, is:
rₛ = 2GM / c²
where:
• G = gravitational constant = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²
• M = mass of the object
• c = speed of light = 299,792,458 m/s
Why is the Event Horizon Radius Important?
Understanding the event horizon radius is fundamental in astrophysics because:
- It determines whether a collapsing star will form a black hole
- It defines the "size" of a black hole (even though black holes have no physical surface)
- It is used to estimate masses of supermassive black holes in galactic centers (e.g., Sagittarius A* has ~4.3 million solar masses → rₛ ≈ 12.7 million km)
- It appears in gravitational lensing calculations and Hawking radiation studies
How to Use This Event Horizon Radius Calculator
- Enter the mass of the celestial object
- Select the unit (Solar masses is most common for black holes)
- Click “Calculate Event Horizon Radius”
- The tool instantly returns the Schwarzschild radius in kilometers, meters, and provides real-world comparisons (e.g., “about 9 times the radius of the Sun”)
Real-World Examples
Here are some known values calculated with this exact formula:
- Sun (1 M☉) → Event horizon radius ≈ 2.95 km
- Earth (1 M⊕) → Event horizon radius ≈ 8.87 mm (size of a grape!)
- Sagittarius A* (4.3 million M☉) → ≈ 12.7 million km (17 times Sun’s radius)
- M87* black hole (6.5 billion M☉) → ≈ 19 billion km (38 AU — larger than Pluto’s orbit)
Scientific Accuracy & Sources
This calculator uses the exact Schwarzschild solution with up-to-date constants recommended by CODATA 2018. All calculations are performed client-side with 64-bit floating-point precision. For in-depth reading, visit the Wikipedia page on Event Horizon Radius.
When Should You Use This Tool?
Use this Event Horizon Radius Calculator when you want to:
- Understand how compact an object must be to become a black hole
- Compare stellar-mass vs supermassive black holes
- Teach or learn general relativity concepts
- Perform quick estimates during research or stargazing sessions
Fun Fact
If you compressed the entire Earth to the size of a peanut (~9 mm), it would collapse into a tiny black hole! The event horizon radius shows just how extreme gravity can be.
Frequently Asked Questions
Is the event horizon the same as the black hole’s actual size?
Yes. The Schwarzschild radius is considered the effective “radius” of a non-rotating black hole.
Does rotation affect the event horizon?
Yes. For spinning (Kerr) black holes, the event horizon is smaller and oblate. This calculator provides the non-rotating (Schwarzschild) case, which is the maximum possible radius.
Can anything escape the event horizon?
No. Once past the event horizon, the escape velocity exceeds the speed of light — impossible according to relativity.
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