Half-Life and Radioactive Decay Calculator
ANA›Life Services Authority›National Calculator Authority›Half-Life and Radioactive Decay 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; } }
Half-Life and Radioactive Decay Calculator
Calculate the remaining quantity of a radioactive substance, its activity, decay constant, or elapsed time using the radioactive decay law.
Solve For
Remaining Quantity (N) Elapsed Time (t) Half-Life (t½) Initial Quantity (N₀) Activity (A)
Initial Quantity (N₀)
grams (g) milligrams (mg) kilograms (kg) atoms
Remaining Quantity (N)
grams (g) milligrams (mg) kilograms (kg) atoms
Half-Life (t½)
seconds (s) minutes (min) hours (hr) days (d) years (yr)
Elapsed Time (t)
seconds (s) minutes (min) hours (hr) days (d) years (yr)
Activity (A)
Becquerel (Bq) Curie (Ci) Megabecquerel (MBq) Gigabecquerel (GBq)
Calculate Results will appear here.
function halUpdateFields() { var mode = document.getElementById("hal-mode").value; var fields = { "hal-field-initial": ["remaining","time","halflife","activity"], "hal-field-remaining": ["time","halflife","initial"], "hal-field-halflife": ["remaining","time","initial","activity"], "hal-field-time": ["remaining","halflife","initial"], "hal-field-activity": ["activity"] }; // Show all first ["hal-field-initial","hal-field-remaining","hal-field-halflife","hal-field-time","hal-field-activity"].forEach(function(id){ document.getElementById(id).style.display = "flex"; }); // Hide the solved-for field if (mode === "remaining") document.getElementById("hal-field-remaining").style.display = "none"; if (mode === "time") document.getElementById("hal-field-time").style.display = "none"; if (mode === "halflife") document.getElementById("hal-field-halflife").style.display = "none"; if (mode === "initial") document.getElementById("hal-field-initial").style.display = "none"; if (mode === "activity") { document.getElementById("hal-field-remaining").style.display = "none"; document.getElementById("hal-field-time").style.display = "none"; document.getElementById("hal-field-activity").style.display = "none"; } }
function halGetVal(id, unitId) { var raw = parseFloat(document.getElementById(id).value); var unitSel = document.getElementById(unitId); var unitVal = unitSel ? unitSel.value : "1"; if (isNaN(raw)) return NaN; if (unitVal === "atoms") return raw; // dimensionless count return raw * parseFloat(unitVal); }
function halFormatNum(val) { if (Math.abs(val) >= 1e6 || (Math.abs(val) " + "Remaining Quantity (N): " + halFormatNum(N) + " " + halUnitLabel("hal-initial-unit") + "" + "Decayed Amount: " + halFormatNum(decayed) + " " + halUnitLabel("hal-initial-unit") + "" + "Percent Remaining: " + pct.toFixed(4) + "%" + "Decay Constant (λ): " + halFormatNum(lambda) + " s⁻¹" + "Activity (A): " + halFormatNum(A) + " Bq (if N in atoms)"; }
else if (mode === "time") { var N0 = halGetVal("hal-initial", "hal-initial-unit"); var N = halGetVal("hal-remaining", "hal-remaining-unit"); var t2 = halGetVal("hal-halflife", "hal-halflife-unit"); if (isNaN(N0)||isNaN(N)||isNaN(t2)) throw new Error("Please fill in all required fields."); if (N0 N0) throw new Error("Remaining quantity cannot exceed initial quantity."); if (t2 " + "Elapsed Time (t): " + halFormatNum(t) + " s" + "Elapsed Time: " + halFormatNum(t/60) + " min | " + halFormatNum(t/3600) + " hr | " + halFormatNum(t/86400) + " days | " + halFormatNum(t/31557600) + " yr" + "Number of Half-Lives Elapsed: " + halvings.toFixed(4) + "" + "Decay Constant (λ): " + halFormatNum(lambda) + " s⁻¹"; }
else if (mode === "halflife") { var N0 = halGetVal("hal-initial", "hal-initial-unit"); var N = halGetVal("hal-remaining", "hal-remaining-unit"); var t = halGetVal("hal-time", "hal-time-unit"); if (isNaN(N0)||isNaN(N)||isNaN(t)) throw new Error("Please fill in all required fields."); if (N0 N0) throw new Error("Remaining quantity cannot exceed initial quantity."); if (t " + "Half-Life (t½): " + halFormatNum(t2) + " s" + "Half-Life: " + halFormatNum(t2/60) + " min | " + halFormatNum(t2/3600) + " hr | " + halFormatNum(t2/86400) + " days | " + halFormatNum(t2/31557600) + " yr" + "Decay Constant (λ): " + halFormatNum(lambda) + " s⁻¹" + "Mean Lifetime (τ = 1/λ): " + halFormatNum(1/lambda) + " s"; }
else if (mode === "initial") { var N = halGetVal("hal-remaining", "hal-remaining-unit"); var t = halGetVal("hal-time", "hal-time-unit"); var t2 = halGetVal("hal-halflife", "hal-halflife-unit"); if (isNaN(N)||isNaN(t)||isNaN(t2)) throw new Error("Please fill in all required fields."); if (N " + "Initial Quantity (N₀): " + halFormatNum(N0) + " " + halUnitLabel("hal-remaining-unit") + "" + "Decayed Amount: " + halFormatNum(decayed) + " " + halUnitLabel("hal-remaining-unit") + "" + "Percent Remaining: " + ((N/N0)*100).toFixed(4) + "%" + "Decay Constant (λ): " + halFormatNum(lambda) + " s⁻¹"; }
else if (mode === "activity") { var N0 = halGetVal("hal-initial", "hal-initial-unit"); var t2 = halGetVal("hal-halflife", "hal-halflife-unit"); if (isNaN(N0)||isNaN(t2)) throw new Error("Please fill in all required fields."); if (N0 " + "Decay Constant (λ): " + halFormatNum(lambda) + " s⁻¹" + "Mean Lifetime (τ): " + halFormatNum(1/lambda) + " s" + "Initial Activity (A₀): " + halFormatNum(A_Bq) + " Bq" + "Initial Activity: " + halFormatNum(A_Ci) + " Ci" + "Initial Activity: " + halFormatNum(A_MBq) + " MBq"; }
} catch(e) { res.innerHTML = "Error: " + e.message + ""; } }
halUpdateFields();
#### Formulas Used
Radioactive Decay Law: N(t) = N₀ · e−λt
Decay Constant: λ = ln(2) / t½ ≈ 0.693147 / t½
Half-Life from measurements: t½ = −t · ln(2) / ln(N/N₀)
Elapsed Time: t = −t½ · ln(N/N₀) / ln(2)
Initial Quantity: N₀ = N · eλt
Activity: A = λ · N (in Becquerels when N is in atoms)
Mean Lifetime: τ = 1/λ = t½ / ln(2)
#### Assumptions & References
- Reference: Rutherford, E. & Soddy, F. (1902). "The Cause and Nature of Radioactivity." Philosophical Magazine.
- Reference: Bateman, H. (1910). "Solution of a system of differential equations." Proc. Cambridge Phil. Soc.
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