Schwarzschild Radius Calculator
Calculate the Schwarzschild radius (event horizon) of a black hole using r_s = 2GM/c². Determine the size of the boundary beyond which nothing, not even light, can escape gravitational pull.
This free online schwarzschild radius calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Schwarzschild Radius Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Schwarzschild Radius Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Schwarzschild Radius Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Schwarzschild Radius Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Schwarzschild Radius Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the Schwarzschild radius (event horizon) of a black hole using r_s = 2GM/c². Determine the size of the boundary beyond which nothing, not even light, can escape gravitational pull. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Schwarzschild Radius Calculator
The Schwarzschild Radius Calculator determines the event horizon radius of a non-rotating black hole — the boundary beyond which the escape velocity exceeds the speed of light. Derived by Karl Schwarzschild in 1916 as the first exact solution to Einstein's field equations of general relativity, this radius defines the ultimate compactness of matter. The Sun compressed to its Schwarzschild radius (about 3 km) would become a black hole. Earth's Schwarzschild radius is just 8.87 mm. Supermassive black holes at galaxy centers can have event horizons larger than our solar system.
The Math Behind It
Formula Reference
Schwarzschild Radius
r_s = 2GM/c²
Variables: G = 6.674×10⁻¹¹ N·m²/kg², M = mass, c = 2.998×10⁸ m/s
Worked Examples
Example 1: Solar Mass Black Hole
M = 1.989×10³⁰ kg (1 solar mass)
Schwarzschild radius of about 3 km for one solar mass.
Example 2: Earth as Black Hole
M = 5.972×10²⁴ kg
Earth would need to be compressed to 8.87 mm radius to become a black hole.
Example 3: Sagittarius A*
M = 4.3 × 10⁶ solar masses = 8.55×10³⁶ kg
Event horizon radius of 12.7 million km — about 0.085 AU.
Common Mistakes & Tips
- !Treating the Schwarzschild radius as a physical surface — it is a boundary in spacetime, not a solid object.
- !Applying this formula to rotating black holes — rotating black holes use the Kerr metric, which has a more complex horizon structure.
- !Assuming anything at the Schwarzschild radius is infinitely dense — the singularity is at r = 0, not at r_s.
Related Concepts
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Frequently Asked Questions
What happens inside a black hole?
Beyond the event horizon, all paths through spacetime lead toward the singularity at r = 0. Time and space effectively swap roles — moving forward in time means moving toward the center, making escape as impossible as traveling backward in time. Our physics breaks down at the singularity itself.
Can Earth become a black hole?
Only if compressed to a radius of 8.87 mm, which requires forces far beyond any known physical process. No natural mechanism can compress Earth-mass objects into black holes. Only stars above about 25 solar masses can collapse into black holes.
Do black holes last forever?
No. Hawking radiation causes black holes to slowly evaporate. However, a solar-mass black hole would take about 10⁶⁷ years to evaporate — vastly longer than the current age of the universe (1.4×10¹⁰ years). Supermassive black holes last even longer.