Use this chemistry calculator to reproduce a named relationship with explicit quantities and units for study, laboratory planning, or an independent numerical check.

Atomic number

Required integer input.

Quantum number

Required integer input.

Calculate the Bohr-model radius of a hydrogen-like atom or ion at a specified principal quantum number. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Bohr radius (m)

The resulting bohr radius returned as a number.

• Introductory quantum formulas usually assume idealized one-electron or particle-in-a-box models. Boundary conditions, dimensionality, electron correlation, relativistic effects, and the selected constants determine whether the approximation applies.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check units and significant figures, compare the result with limiting cases, and use measured or source-specific constants where available. Laboratory, safety, and regulatory decisions require validated methods and appropriate uncertainty analysis.

• Ionization Energy Rydberg Calculator

  Calculate the hydrogen-like ionization energy from a principal quantum level using the Rydberg relation.

• Rydberg Wavelength Calculator

  Calculate the wavelength of a hydrogen-like electronic transition using the Rydberg formula.

• Packing Fraction Calculator

  Calculate the hard-sphere packing fraction of a unit cell from atomic radius, atom count, and unit-cell volume.