Primary formula
N = N0 x (1/2)^(t / T_half).
Physics calculator
Radioactive Decay Calculator
Calculate remaining amount and decayed amount using a simplified exponential half-life model.
Last reviewed: July 21, 2026Physics formula engine v3.0.0
Physics calculator
Radioactive Decay Calculator
Enter values, select units and calculate locally. Results use SI internally and show rounded display values.
Decimal.js physics math
Mode
Find remaining amount from initial amount, half-life and elapsed time.
Result and visual stay hidden until you choose Calculate.
Formula and assumptions
Input assumptions
Initial amount is nonnegative. Half-life is greater than zero. Elapsed time is nonnegative.
Precision note
Physics calculators convert compatible inputs into SI units before calculating. Decimal.js is used for arithmetic where practical; trigonometric angle factors are rounded for display.
Physics calculation flow
Parse
Read labelled inputs, selected units and calculation mode from the calculator card.
Convert
Convert compatible values to SI base or derived units without calling external services.
Calculate
Apply the selected deterministic mechanics formula and validate against NaN, Infinity and invalid divisors.
Label
Display the result, supporting unit rows, formula steps, warnings and dynamic visual below the input card.
What Radioactive Decay Calculator does
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known.
The calculator is deterministic and runs from manual inputs only. It is a physics formula tool, so it should not be confused with a unit converter that only changes labels after a value is already known.
Formula and variables
N = N0 x (1/2)^(t / T_half).
The calculator converts supported units into SI base or derived units for the actual calculation, then formats the result in the selected display unit.
- N is remaining amount
- N0 is initial amount
- t is elapsed time
- T_half is half-life
Worked examples
Use the examples below to check expected order of operations and unit handling before applying the tool to your own values.
- 1000 with half-life 10 days and time 30 days gives 125 remaining
- Two half-lives leave 25 percent
- Zero elapsed time leaves the initial amount unchanged.
Unit conversions
Length, time, mass, area, volume, speed, force, pressure, density, frequency, energy and power units reuse the central NexaCalc conversion registry. Acceleration, angle and spring-constant units use the same SI-first convention where applicable.
The displayed conversion rows are supporting context. They do not change the physical assumptions of the selected formula.
Common mistakes
Most errors come from mixing physical quantities that sound similar in everyday language or choosing a unit that belongs to a different dimension.
- Using calendar dates instead of elapsed duration.
- Mixing half-life time units.
- Treating remaining amount as radiation dose or safety level.
Assumptions and limitations
This page is intended for educational and planning calculations, not professional engineering certification.
This calculator uses idealized physics formulas and the input values you provide. Real systems may require additional effects such as friction, drag, rotation, deformation, losses or measurement uncertainty.
- Initial amount is nonnegative.
- Half-life is greater than zero.
- Elapsed time is nonnegative.
- This calculator does not model decay chains, biological half-life, shielding, dose or regulatory limits.
- Decay constants are assumed constant.
Frequently asked questions
How is radioactive decay calculated?
Radioactive Decay Calculator uses N = N0 x (1/2)^(t / T_half). The result is calculated from the values and units entered in the form.
What does half-life mean?
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known. Initial amount is nonnegative.
How much remains after three half-lives?
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known. Initial amount is nonnegative.
Can initial amount be zero?
Radioactive Decay Calculator allows signed results only where the physics quantity can carry direction or reference-sign meaning. Divisors such as time, mass and gravity are validated before calculation.
What time units are supported?
Radioactive Decay Calculator converts compatible inputs to SI internally, then displays the selected output unit. N is remaining amount; N0 is initial amount; t is elapsed time; T_half is half-life.
Is this the same as radiation dose?
Radioactive Decay Calculator is formula-based. Use the related calculator when the question changes physical quantity, and use Conversion tools only when the value is already known.
Does this calculator model decay chains?
Radioactive Decay Calculator uses an idealized classroom physics model. This calculator does not model decay chains, biological half-life, shielding, dose or regulatory limits.
How is this different from Half-Life Calculator?
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known. Initial amount is nonnegative.
Can this calculator be used for medical decisions?
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known. Initial amount is nonnegative.
Why is radioactive decay exponential?
Use this calculator for educational radioactive-decay examples when initial amount, half-life and elapsed time are known. Initial amount is nonnegative.
References
- NIST Special Publication 811, Guide for the Use of the International System of Units. Relevance: SI unit symbols and derived-unit naming. Last verified: July 21, 2026. Source.
- BIPM, The International System of Units SI Brochure. Relevance: SI base and derived units used in mechanics, fluids, waves and optics. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 1. Relevance: introductory formulas for motion, force, work, energy, momentum, fluids, waves and optics. Last verified: July 21, 2026. Source.
- NIST CODATA internationally recommended values. Relevance: physical constants for electricity, modern physics, gravitation and radiation formulas. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 2. Relevance: electric circuits, capacitance, magnetic force and electromagnetic waves. Last verified: July 21, 2026. Source.
- OpenStax University Physics Volume 3. Relevance: photons, nuclear decay and blackbody radiation concepts. Last verified: July 21, 2026. Source.
Physics references verified for SI units, mechanics, fluids, waves, sound and optics formulas on July 21, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.