Schwarzschild Radius Calculator
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.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Schwarzschild Radius Calculator
Calculate the Schwarzschild radius — the critical radius at which a mass becomes a black hole. If an object is compressed within this radius, not even light can escape its gravitational pull.
Mass
Kilograms (kg) Solar Masses (M☉) Earth Masses (M⊕) Grams (g) Metric Tons (t)
Enter the mass of the object you want to analyze.
Output Unit
Meters (m) Kilometers (km) Centimeters (cm) Millimeters (mm) Micrometers (μm) Nanometers (nm) Astronomical Units (AU) Light-Years (ly)
Calculate Schwarzschild Radius
function schCalc() { const resultDiv = document.getElementById('sch-result'); const errorDiv = document.getElementById('sch-error'); resultDiv.style.display = 'none'; errorDiv.style.display = 'none';
const massInput = document.getElementById('sch-mass').value.trim(); const unit = document.getElementById('sch-unit').value; const outUnit = document.getElementById('sch-outunit').value;
// --- Validation --- if (massInput === '' || isNaN(massInput)) { errorDiv.textContent = 'Please enter a valid numeric mass.'; errorDiv.style.display = 'block'; return; } const massRaw = parseFloat(massInput); if (massRaw ' + exp + ''; }
// --- Context comparison --- const sunRs = 2953.25; // m — Schwarzschild radius of the Sun const earthRs = 0.008871; // m — Schwarzschild radius of the Earth let context = ''; if (rs_m > 0) { const ratioSun = rs_m / sunRs; const ratioEarth = rs_m / earthRs; if (ratioSun >= 0.01) { context = '≈ ' + ratioSun.toPrecision(4) + ' × the Schwarzschild radius of the Sun (' + fmtSci(sunRs) + ' m)'; } else if (ratioEarth >= 0.01) { context = '≈ ' + ratioEarth.toPrecision(4) + ' × the Schwarzschild radius of Earth (' + fmtSci(earthRs) + ' m)'; } }
// --- Display --- resultDiv.innerHTML = 'Schwarzschild Radius: ' + fmtSci(rs_out) + ' ' + conv.label + '= ' + fmtSci(rs_m) + ' m (in meters)' + context; resultDiv.style.display = 'block'; }
// Allow Enter key to trigger calculation document.addEventListener('DOMContentLoaded', function() { document.getElementById('sch-mass').addEventListener('keydown', function(e) { if (e.key === 'Enter') schCalc(); }); });
#### Formula
rs = 2GM / c²
- rs — Schwarzschild radius (m)
- G — Gravitational constant = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²
- M — Mass of the object (kg)
- c — Speed of light in vacuum = 2.99792458 × 10⁸ m/s
This formula is derived from Karl Schwarzschild's 1916 exact solution to Einstein's field equations of general relativity for a non-rotating, spherically symmetric mass.
#### Assumptions & References
- The object is assumed to be non-rotating and uncharged (Schwarzschild metric). Rotating black holes require the Kerr metric; charged ones require the Reissner–Nordström metric.
- The result is the event horizon radius — the boundary inside which escape velocity exceeds the speed of light.
- Reference: Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften.
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