# Radioactive Half-Life Calculator

Free half-life calculator. Calculate remaining quantity, elapsed time, or half-life for radioactive decay. Uses N = N₀(1/2)^(t/t½).

## What this calculates

Calculate radioactive decay using the half-life formula: N = N₀ × (1/2)^(t/t½). Find the remaining quantity, elapsed time, half-life, or initial quantity.

## Inputs

- **Solve For** — options: Remaining Quantity (N), Elapsed Time (t), Half-Life (t½), Initial Quantity (N₀) — Select what to calculate.
- **Initial Quantity (N₀)** — min 0 — Initial amount (grams, atoms, activity, etc.).
- **Remaining Quantity (N)** — min 0 — Amount remaining after decay.
- **Half-Life (t½)** — min 0 — Half-life in your chosen time unit.
- **Elapsed Time (t)** — min 0 — Time elapsed (same unit as half-life).
- **Time Unit** — options: Seconds, Minutes, Hours, Days, Years — Unit for both half-life and elapsed time.

## Outputs

- **Result** — The calculated value.
- **Unit** — formatted as text — Unit of the result.
- **Percent Remaining** — Percentage of original quantity remaining.
- **Number of Half-Lives** — How many half-lives have elapsed.
- **Formula** — formatted as text — Step-by-step calculation.

## Frequently Asked Questions

**Q: What is a half-life?**

A: A half-life (t½) is the time required for half of a radioactive substance to decay. After one half-life, 50% remains; after two half-lives, 25% remains; after three, 12.5%, and so on.

**Q: Does half-life depend on the amount of substance?**

A: No. Half-life is a characteristic property of each radioactive isotope and does not depend on the amount present. Whether you start with 1 gram or 1 kilogram, the same fraction decays in each half-life period.

**Q: What are some common half-lives?**

A: Carbon-14: 5,730 years (used in carbon dating). Uranium-238: 4.5 billion years. Iodine-131: 8 days (medical use). Polonium-214: 164 microseconds. Cobalt-60: 5.27 years (radiation therapy).

**Q: What is the relationship between half-life and decay constant?**

A: The decay constant (λ) = ln(2) / t½ = 0.693 / t½. The decay constant is the probability of decay per unit time and appears in the exponential form: N = N₀ × e^(-λt).

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Source: https://vastcalc.com/calculators/chemistry/half-life
Category: Chemistry
Last updated: 2026-04-21