Stellar Luminosity Calculator
ANA›Life Services Authority›National Calculator Authority›Stellar Luminosity Calculator
.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; } }
Stellar Luminosity Calculator
Calculate the luminosity of a star relative to the Sun using the Stefan-Boltzmann law, given its radius and surface temperature.
Stellar Radius (in Solar Radii, R☉)
Surface Temperature (Kelvin)
Output Mode
Relative to Sun (L☉) Absolute (Watts)
Calculate Results will appear here.
function stecalc() { var resultDiv = document.getElementById('ste-result'); var R = parseFloat(document.getElementById('ste-radius').value); var T = parseFloat(document.getElementById('ste-temp').value); var mode = document.getElementById('ste-mode').value;
// Input validation if (isNaN(R) || isNaN(T)) { resultDiv.innerHTML = 'Please enter valid numbers for both radius and temperature.'; return; } if (R Stellar radius must be greater than zero.'; return; } if (T Surface temperature must be greater than zero Kelvin.'; return; } if (T Temperature seems unrealistically low. Please enter a value above 100 K.'; return; } if (T > 2e6) { resultDiv.innerHTML = 'Temperature exceeds realistic stellar surface values (max ~2,000,000 K). Please check your input.'; return; } if (R > 2000) { resultDiv.innerHTML = 'Radius exceeds realistic stellar values (max ~2000 R☉). Please check your input.'; return; }
// Constants var T_sun = 5778; // Solar surface temperature in Kelvin var R_sun_m = 6.957e8; // Solar radius in meters var sigma = 5.670374419e-8; // Stefan-Boltzmann constant W m^-2 K^-4 var L_sun = 3.828e26; // Solar luminosity in Watts
// Stefan-Boltzmann Law: L = 4 * pi * R^2 * sigma * T^4 // Relative to Sun: L/L_sun = (R/R_sun)^2 * (T/T_sun)^4
var L_solar = Math.pow(R, 2) * Math.pow(T / T_sun, 4); var L_watts = 4 * Math.PI * Math.pow(R * R_sun_m, 2) * sigma * Math.pow(T, 4);
// Absolute magnitude (visual approximation using bolometric) // M_bol = M_bol_sun - 2.5 * log10(L/L_sun), M_bol_sun = 4.74 var M_bol_sun = 4.74; var M_bol = M_bol_sun - 2.5 * Math.log10(L_solar);
// Format numbers nicely function fmt(n, sig) { if (Math.abs(n) >= 1e4 || (Math.abs(n) '; html += 'ParameterValue'; html += 'Luminosity (L☉)' + fmt(L_solar, 5) + ' L☉'; html += 'Luminosity (Watts)' + L_watts.toExponential(4) + ' W'; html += 'Bolometric Absolute Magnitude' + M_bol.toFixed(3) + ''; html += 'Input Radius' + R + ' R☉ (' + (R * R_sun_m / 1000).toExponential(3) + ' km)'; html += 'Input Temperature' + T.toLocaleString() + ' K';
// Star classification hint var starType = ''; if (T >= 30000) starType = 'O-type (blue, very hot)'; else if (T >= 10000) starType = 'B-type (blue-white)'; else if (T >= 7500) starType = 'A-type (white)'; else if (T >= 6000) starType = 'F-type (yellow-white)'; else if (T >= 5200) starType = 'G-type (yellow, like the Sun)'; else if (T >= 3700) starType = 'K-type (orange)'; else starType = 'M-type (red dwarf)'; html += 'Spectral Class (approx.)' + starType + ''; html += '';
resultDiv.innerHTML = html; }
#### Formula
Stefan-Boltzmann Law:
L = 4π R² σ T⁴
Where:
- L = Stellar luminosity (Watts)
- R = Stellar radius (meters)
- σ = Stefan-Boltzmann constant = 5.6704 × 10⁻⁸ W m⁻² K⁻⁴
- T = Effective surface temperature (Kelvin)
Relative to the Sun:
L / L☉ = (R / R☉)² × (T / T☉)⁴
Where T☉ = 5,778 K and R☉ = 6.957 × 10⁸ m.
Bolometric Absolute Magnitude:
M_bol = 4.74 − 2.5 × log₁₀(L / L☉)
#### Assumptions & References
- References: Carroll & Ostlie, Introduction to Modern Astrophysics; IAU 2015 Resolution B3.
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