Calculator Inputs
Example Data Table
The following sample values use the empirical constant r0 = 1.20 fm.
| Nucleus | Mass Number (A) | r0 (fm) | Radius (fm) | Diameter (fm) | Volume (fm³) |
|---|---|---|---|---|---|
| Hydrogen-1 | 1 | 1.20 | 1.200 | 2.400 | 7.238 |
| Helium-4 | 4 | 1.20 | 1.905 | 3.810 | 28.953 |
| Carbon-12 | 12 | 1.20 | 2.747 | 5.495 | 86.859 |
| Iron-56 | 56 | 1.20 | 4.591 | 9.182 | 405.341 |
| Uranium-238 | 238 | 1.20 | 7.437 | 14.873 | 1,722.699 |
Formula Used
The calculator uses the empirical nuclear size relation R = r0A1/3, where R is the nuclear radius, r0 is the nuclear radius constant, and A is the mass number.
Additional outputs use standard sphere relationships: D = 2R, Surface Area = 4πR², and Volume = (4/3)πR³.
The density estimate assumes a roughly uniform spherical nucleus and multiplies the mass number by an average nucleon mass. Charge density is estimated only when the atomic number is supplied.
How to Use This Calculator
- Enter the nucleus label for easy identification.
- Provide the mass number A for the isotope or nucleus.
- Optionally enter atomic number Z to estimate charge density.
- Choose a preset model or set a custom radius constant.
- Add an uncertainty if you want an uncertainty band.
- Enter a comparison mass number to compare two nuclei.
- Pick the preferred output unit and decimal precision.
- Press the calculate button to view the results and graph.
- Use the CSV and PDF buttons to save your work.
Frequently Asked Questions
1) What does the nuclear radius formula represent?
It gives an empirical estimate of nuclear size using the mass number. The cube-root dependence reflects how nuclear volume grows nearly proportionally with the number of nucleons.
2) Why is the exponent one-third?
If nuclei behave like roughly constant-density spheres, volume scales with nucleon count. Radius therefore scales with the cube root of the mass number.
3) What is a typical value for r0?
A common value is about 1.2 femtometres. Some models use slightly smaller or larger constants for light or heavy nuclei.
4) Is this calculator exact for every isotope?
No. It is a strong approximation for many nuclei, but shell effects, deformation, and measurement methods can shift real values from the simple empirical estimate.
5) Why include atomic number Z?
Atomic number lets the calculator estimate charge density under a uniform-charge assumption. Radius itself is mainly determined here from the mass number and radius constant.
6) What does the density result mean?
It is an approximate average nuclear density from a spherical model. It helps show why nuclear matter remains extremely dense across many isotopes.
7) Why compare two mass numbers?
Comparing two nuclei quickly shows how slowly radius increases as mass number grows. Large increases in nucleon count produce only moderate radius changes.
8) What unit should I use for nuclear size?
Femtometres are the most practical unit for nuclear dimensions. The calculator also shows metre-scale values for completeness and scientific reporting.