Radioactivity Calculator: Ci, Bq, cpm, dpm and Decay Correction

This page is for bench scientists who need to convert radioactivity units, turn counter readings into activity, or decay-correct a stock. The short answer: 1 Bq is one decay per second, 1 Ci is exactly 3.7 × 10¹⁰ Bq, counts per minute (cpm) become decays per minute (dpm) by dividing by counting efficiency, and remaining activity is A = A₀ × 0.5^(t / half-life). A web page cannot run a live calculator, so the tables, formulas and copy-ready code below do the same job and show every step.

This is arithmetic only. Follow your institution’s radiation safety officer, licence conditions and procedures for handling, records and disposal.

Units and conversions: Ci, Bq and dpm

The becquerel (Bq) is the SI unit of activity: one disintegration per second (US NRC glossary, Becquerel). The NRC glossary also states that 3.7 × 10¹⁰ Bq equals 1 curie (Ci), and NIST SP 811, Appendix B.8 lists the curie-to-becquerel factor of 3.7 × 10¹⁰ as exact (NIST Guide to the SI, Appendix B.8, read 2026-11-07). NIST notes the curie is a non-SI unit; many labs and licences still use it. Because 1 Bq = 1 dps, 1 Bq = 60 dpm.

Unit	Bq	dpm
1 Ci	3.7 × 10¹⁰	2.22 × 10¹²
1 mCi	3.7 × 10⁷ (37 MBq)	2.22 × 10⁹
1 µCi	3.7 × 10⁴ (37 kBq)	2.22 × 10⁶
1 nCi	37	2,220
1 Bq	1	60

The dpm column is derived arithmetically (Bq × 60). To convert, multiply by the row factor; to go from dpm to µCi, divide by 2.22 × 10⁶. For other non-SI units, NIST gives exact factors of 1 rad = 0.01 Gy and 1 rem = 0.01 Sv; those are dose units, not activity units, so they do not convert activity. This is also why a search for a “rad calculator” can mean two different things: a dose-unit conversion (rad to gray), or a decay calculator that happens to be named RAD. Check whether you hold activity (Ci, Bq, dpm) or dose (rad, Gy, rem, Sv) before converting.

cpm vs dpm: the counting-efficiency step

A counter reports counts per minute (cpm), the events it detected, not the decays that occurred. Decays per minute is: dpm = (cpm_sample − cpm_background) ÷ efficiency, where efficiency is a fraction between 0 and 1. Efficiency depends on the instrument, the isotope, the geometry and, in liquid scintillation counting, the quench level of each sample, so it must come from your own instrument’s calibration or quench curve. It is not a constant you can look up. Calculators that ask for cpm and return dpm are applying exactly this division, so the answer is only as good as the efficiency you enter.

Decay-correction formula

Activity falls exponentially: A = A₀ × e^(−λt), where λ = ln 2 ÷ T_½. This is equivalent to A = A₀ × 0.5^(t ÷ T_½), and t and T_½ must be in the same unit. The relation A = λN links activity to the number of radioactive atoms N, which is the “A = λN” form some calculators use. To correct a reading back to a reference date, divide by the fraction remaining instead of multiplying.

Half-life and fraction-remaining table for common lab nuclides

Half-lives are from the evaluated nuclear structure data served by the National Nuclear Data Center (Brookhaven) NuDat database, read 2026-11-07, rounded to three or four significant figures. Fractions remaining are computed from those half-lives with 0.5^(t ÷ T_½) and rounded to three significant figures.

Nuclide	Half-life	Decay mode	1 d	7 d	14 d	30 d	60 d
H-3	12.32 y	β⁻	1.00	0.999	0.998	0.995	0.991
C-14	5700 y	β⁻	1.00	1.00	1.00	1.00	1.00
P-32	14.27 d	β⁻	0.953	0.712	0.507	0.233	0.0542
P-33	25.38 d	β⁻	0.973	0.826	0.682	0.441	0.194
S-35	87.37 d	β⁻	0.992	0.946	0.895	0.788	0.621
I-125	59.40 d	electron capture	0.988	0.922	0.849	0.705	0.497
Cr-51	27.70 d	electron capture	0.975	0.839	0.704	0.472	0.223

Decay modes are those NNDC lists at 100% for each nuclide. Your supplier’s certificate gives the reference date and calibration activity for your own lot.

Worked examples

Example 1: decay-correct a P-32 stock

Illustrative numbers: a P-32 stock was 100 µCi on its reference date. What is it 21 days later? Fraction remaining = 0.5^(21 ÷ 14.266) = 0.360. Activity = 100 × 0.360 = 36.0 µCi (1.33 MBq).

Example 2: convert cpm to dpm and µCi

Illustrative numbers: a vial reads 5,400 cpm; background is 60 cpm; the counting efficiency for this isotope and geometry was measured at 45% (0.45). Net cpm = 5,340. dpm = 5,340 ÷ 0.45 = 11,867. Then Bq = 11,867 ÷ 60 = 198, and µCi = 11,867 ÷ 2.22 × 10⁶ = 0.00535 µCi (5.35 nCi).

How to compute this in Excel, R or Python

Excel: with half-life in B1, elapsed time in B2 (same unit) and starting activity in B3, enter =B3*0.5^(B2/B1). For dpm from cpm, =(cpm-bkg)/eff.

R:

remaining <- function(a0, t, half_life) a0 * 0.5^(t / half_life)
remaining(100, 21, 14.266)   # 36.0
dpm <- function(cpm, bkg, eff) (cpm - bkg) / eff
dpm(5400, 60, 0.45)          # 11866.67

Python:

def remaining(a0, t, half_life):
    return a0 * 0.5 ** (t / half_life)

def dpm(cpm, bkg, eff):
    return (cpm - bkg) / eff

print(remaining(100, 21, 14.266))  # 36.0
print(dpm(5400, 60, 0.45))         # 11866.67

Frequently asked questions

How do I calculate radioactivity from cpm?

Subtract background cpm from the sample cpm, then divide by the counting efficiency (as a fraction) to get dpm. Divide dpm by 60 for Bq, or by 2.22 × 10⁶ for µCi.

What is a dpm radioactivity calculator doing?

It applies dpm = net cpm ÷ efficiency. Efficiency must be measured for your instrument and sample type.

How many Bq is one curie?

Exactly 3.7 × 10¹⁰ Bq (NIST SP 811, Appendix B.8; NRC glossary).

What is the equation for radioactivity?

Activity A = λN, with λ = ln 2 ÷ half-life, and decay over time follows A = A₀ × 0.5^(t ÷ T_½).

Related pages

• Radioactive waste disposal and decay-in-storage
• Radiation survey meter calibration and response checks
• Radiation safety officer role and responsibilities
• ALARA: time, distance and shielding
• SI units in scientific writing