# Calculator

(formerly accessible on: www.nuk.bieganski.org)

### General math & medicine options

Arithmetic mean and standard deviation
Regression of points to straight line, correlation coefficient
Finding of natural divisors
The highest common divisor
Quadratic equation
Time difference
Estimation of some human biometric parameters
Concentration conversion
### Calculations related to nuclear physics

**Examples of application of the programs below are accessible here**.

Simple radioactive decay (1 radioactive nuclide: A → B)

Successive radioactive decay (2 radioactive nuclides: A → B → C)

Successive radioactive decay (3 radioactive nuclides: A → B → C → D)

Conversion of activity units (traditional into SI-derived and vice versa)

Conversion of mass into activity and vice versa (mass-units into activity-units and vice versa)

### Calculations related to nuclear medicine

**Instruction for the programs below is accessible here**.

(1.)

Calculation of thyroid volumen on the basis of the lobes diameters

(2.)

Calculation of (radio)nuclide uptake (f.e. uptake of radioiodine in the thyroid)

(2a.)

Calculation of uptake of I-131 in the thyroid (This program can be saved as a file and launched in another PC, a browser with HTML and

*JavaScript* is necessary; in Polish).

(3.)

Calculation of radioiodine dose (simplified)

(4.)

Kinetic modeling I. (effective half-time, maximal uptake and others, based on a series of measures) - for radionuclide therapy

(5.)

Kinetic modeling II. (effective half-time, maximal uptake and others, based on three measures) - for radionuclide therapy

(6.)

Calculation of dose of radioiodine or another radionuclide for treatment (modified Marinelli-formula)

(7.)

Dosimetry of α- and β-radiation
(8.)

Dose rate and absorbed dose of γ radiation (in a distance from a point source)

## Simple radioactive decay

Here, you can calculate the remaining quantity (after specified time) of the nuclide 1 with specified physical half-time. The nuclide 1 decays to the nuclide(s) 2 according to the equation:

nuclide 1 → nuclide 2.

The half time of the nuclide and the time elapsed have to be entered **in the same units**. It is also possible to calculate a quantity of the nuclide before the calibration time - in such a case, the time elapsed should be written with the minus (-) sign. A chart will be dynamically generated to the result.

Because the quantity of the (only) nuclide 1 (number of atoms, moles, mass) is proportional to its activity, the quantity can be expressed as activity. In such a case, however, the calculated quantity of the products (nuclide 2) **should be neglected as false**.

If you need to calculate the time difference between two time points (time elapsed), this algorithm can be helpful.

Symbols used:

T

_{(1/2)1} - physical half time of the nuclide 1

t - time elapsed

N

_{(0)1} - quantity of the nuclide 1 at the beginning (for

*t=0*)

N

_{(t)1} - quantity of the nuclide 1 after time

*t*
τ

_{1} - mean life time of the nuclide 1

λ

_{1} - decay constant of the nuclide 1

D

_{f} - decay factor (the fraction of the nuclide 1 which remains from the primary quantity due to the physical decay after the time

*t*)