Can I solve for different variables?

Yes! This calculator supports reverse solving. You can solve for: Activity, Na, Half-life, Sample mass, Molar mass of the substance, Specific activity.

Radioactive decay

Solve radioactive decay relationships quickly using core chemistry formulas.

Formula shown5 inputs definedUpdated Nov 2025By Automated Chemistry GeneratorFree, no sign-up

Quick Summary

Use this when you need:

Project how much isotope remains after shipping or storage
Fit experimental decay data to extract λ
Translate between half-life and remaining activity for safety planning

You’ll need:Na, Half-life, Sample mass, Molar mass of the substance, and 1 more

You’ll get:Activity

How this is calculated

Formula:

N(t) = N0 · e^(-λ t)

In plain language:

Radioactive decay follows first-order kinetics, so multiplying the initial amount N0 by e to the minus decay constant λ times elapsed time t gives the remaining quantity at time t.

The formula is always visible so you can verify the math and explain your numbers to anyone who asks.

What these terms mean

Activity

Activity used in the calculation.

Na

Na used in the calculation.

Half-life

Half-life used in the calculation.

Sample mass

Sample mass used in the calculation.

Molar mass of the substance

Molar mass of the substance used in the calculation.

Specific activity

Specific activity used in the calculation.

When to use this calculator

Project how much isotope remains after shipping or storage
Fit experimental decay data to extract λ
Translate between half-life and remaining activity for safety planning

Last updated: November 19, 2025

Radioactive decay calculator explained

Activity ( $A$ ) equals the number of nuclei ( $N$ ) multiplied by the decay constant $\\lambda$ . For a pure isotope, $N = \\frac{m}{M} N_A$ , so
$A = \\frac{m}{M} N_A \\frac{\\ln 2}{t_{1/2}}$ .
This calculator accepts the Avogadro constant {na}, sample mass {mass}, molar mass {mmol}, and half-life {halflife} to output activity {activity} and specific activity {spec_activity}.

Use it to plan handling of sealed sources, convert procurement masses into Becquerels, or estimate decay rates for tracer studies.

How the conversion works

Key relationships:

A = N \\lambda = \\frac{m}{M} N_A \\frac{\\ln 2}{t_{1/2}}, \\qquad a_{\\text{sp}} = \\frac{A}{m}

where $m$ is sample mass, $M$ is molar mass, $N_A$ is Avogadro's number, and $t_{1/2}$ is half-life (use seconds if you want $A$ in Bq). The calculator treats {na} as $N_A$ and reports both total and specific activity.

Units and conversions

Quantity	Units	Notes
Mass $m$	g	Convert mg to g before entering.
Molar mass $M$	g/mol	Use the isotope's atomic mass.
$N_A$	mol $^{-1}$	Typically $6.02214076 \\times 10^{23}$ .
Half-life $t_{1/2}$	s, min, h, days	Keep consistent with desired activity units.
Activity $A$	Bq (if $t_{1/2}$ in s) or Ci (after conversion)	$1\\ \\text{Ci} = 3.7 \\times 10^{10}\\ \\text{Bq}$ .
Specific activity	activity per gram	Useful for labeling efficiency.

Worked examples

Activity of I-131 sample
$m = 0.150\\ \\text{g}$ , $M = 131\\ \\text{g}\\,\\text{mol}^{-1}$ , $t_{1/2} = 8.02\\ \\text{days} = 6.93 \\times 10^{5}\\ \\text{s}$ , $N_A = 6.022 \\times 10^{23}\\ \\text{mol}^{-1}$ .

A = \\frac{0.150}{131} \\times 6.022 \\times 10^{23} \\times \\frac{\\ln 2}{6.93 \\times 10^{5}} = 5.45 \\times 10^{11}\\ \\text{Bq}

Convert to curies: $A = 14.7\\ \\text{Ci}$ .

Specific activity of Co-57 standard
$M = 57.0\\ \\text{g}\\,\\text{mol}^{-1}$ , $t_{1/2} = 271.8\\ \\text{days} = 2.35 \\times 10^{7}\\ \\text{s}$ .

a_{\\text{sp}} = \\frac{N_A \\ln 2}{M t_{1/2}} = 3.17 \\times 10^{12}\\ \\text{Bq}\\,\\text{g}^{-1}

Multiply by sample mass to get total activity.

Tips and pitfalls

Always convert half-life to seconds when you want activity in Becquerels; otherwise scale by the conversion factor.
Correct the sample mass for isotopic purity; natural elements contain multiple isotopes that dilute the activity.
Propagate uncertainties in half-life, mass, and weighing to understand overall activity uncertainty.
Use decay-correction factors $A(t) = A_0 e^{-\\lambda t}$ to project activity at future times after computing $A_0$ .

References and further reading

Frequently Asked Questions

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Calculator info

Version:: v1.0.0
Last reviewed:: Nov 15, 2025
Sensitivity:: low
References:: 1

Last updated: November 19, 2025

Radioactive decay calculator explained

Use it to plan handling of sealed sources, convert procurement masses into Becquerels, or estimate decay rates for tracer studies.

How the conversion works

Key relationships:

A = N \\lambda = \\frac{m}{M} N_A \\frac{\\ln 2}{t_{1/2}}, \\qquad a_{\\text{sp}} = \\frac{A}{m}

Units and conversions

Quantity	Units	Notes
Mass $m$	g	Convert mg to g before entering.
Molar mass $M$	g/mol	Use the isotope's atomic mass.
$N_A$	mol $^{-1}$	Typically $6.02214076 \\times 10^{23}$ .
Half-life $t_{1/2}$	s, min, h, days	Keep consistent with desired activity units.
Activity $A$	Bq (if $t_{1/2}$ in s) or Ci (after conversion)	$1\\ \\text{Ci} = 3.7 \\times 10^{10}\\ \\text{Bq}$ .
Specific activity	activity per gram	Useful for labeling efficiency.

Worked examples

Activity of I-131 sample
$m = 0.150\\ \\text{g}$ , $M = 131\\ \\text{g}\\,\\text{mol}^{-1}$ , $t_{1/2} = 8.02\\ \\text{days} = 6.93 \\times 10^{5}\\ \\text{s}$ , $N_A = 6.022 \\times 10^{23}\\ \\text{mol}^{-1}$ .

A = \\frac{0.150}{131} \\times 6.022 \\times 10^{23} \\times \\frac{\\ln 2}{6.93 \\times 10^{5}} = 5.45 \\times 10^{11}\\ \\text{Bq}

Convert to curies: $A = 14.7\\ \\text{Ci}$ .

Specific activity of Co-57 standard
$M = 57.0\\ \\text{g}\\,\\text{mol}^{-1}$ , $t_{1/2} = 271.8\\ \\text{days} = 2.35 \\times 10^{7}\\ \\text{s}$ .

a_{\\text{sp}} = \\frac{N_A \\ln 2}{M t_{1/2}} = 3.17 \\times 10^{12}\\ \\text{Bq}\\,\\text{g}^{-1}

Multiply by sample mass to get total activity.

Tips and pitfalls

Always convert half-life to seconds when you want activity in Becquerels; otherwise scale by the conversion factor.
Correct the sample mass for isotopic purity; natural elements contain multiple isotopes that dilute the activity.
Propagate uncertainties in half-life, mass, and weighing to understand overall activity uncertainty.
Use decay-correction factors $A(t) = A_0 e^{-\\lambda t}$ to project activity at future times after computing $A_0$ .

Quick Summary

Calculator Tool

How this is calculated

What these terms mean

Activity

Na

Half-life

Sample mass

Molar mass of the substance

Specific activity

When to use this calculator

Radioactive decay calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

Molarity

Mole

Reconstitution

Molar mass of gas

pKa

Beer-Lambert law

Was this calculator helpful?

Found an error?

Calculator info

Radioactive decay calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

Molarity

Mole

Reconstitution

Molar mass of gas

pKa

Beer-Lambert law

Was this calculator helpful?

Found an error?

Calculator info