Primary formula
N = N0 / 2^n; N = N0 x (1/2)^(t / T_half).
Physics calculator
Half-Life Calculator
Calculate remaining amount after a given number of half-lives, or from half-life duration and elapsed time.
Last reviewed: July 21, 2026Physics formula engine v3.0.0
Physics calculator
Half-Life 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 an entered half-life count.
Result and visual stay hidden until you choose Calculate.
Formula and assumptions
Input assumptions
Initial amount is nonnegative. Number of half-lives is nonnegative. The decay process has a constant half-life.
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 Half-Life Calculator does
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline.
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 / 2^n; 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
- n is number of half-lives
- T_half is half-life duration
Worked examples
Use the examples below to check expected order of operations and unit handling before applying the tool to your own values.
- 800 after 3 half-lives gives 100
- 1000 after 30 days with 10-day half-life gives 125
- One half-life leaves 50 percent.
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.
- Counting elapsed half-lives incorrectly.
- Using percent remaining as amount without converting.
- Applying one half-life to a mixed decay chain.
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.
- Number of half-lives is nonnegative.
- The decay process has a constant half-life.
- This tool is not radiation-safety, medical, nuclear engineering or regulatory guidance.
- It does not model daughter products or background radiation.
Frequently asked questions
How do I calculate remaining amount after half-lives?
Half-Life Calculator uses N = N0 / 2^n; N = N0 x (1/2)^(t / T_half). The result is calculated from the values and units entered in the form.
What does three half-lives mean?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. Initial amount is nonnegative.
How is half-life related to radioactive decay?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. Initial amount is nonnegative.
Can I use elapsed time instead of half-life count?
Half-Life 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.
Why does each half-life halve the remaining amount?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. Initial amount is nonnegative.
Can amount become exactly zero?
Half-Life 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?
Half-Life Calculator converts compatible inputs to SI internally, then displays the selected output unit. N is remaining amount; N0 is initial amount; n is number of half-lives; T_half is half-life duration.
Does this calculator handle decay chains?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. Initial amount is nonnegative.
How is this different from Radioactive Decay Calculator?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. Initial amount is nonnegative.
Is this calculator radiation-safety guidance?
Use this calculator when the problem is stated in half-life intervals or needs a direct half-life timeline. 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.