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Atomic Radius Trend Calculator

Work out atomic radius trend instantly with clear inputs, formula shown and shareable results.

About Atomic Radius Trend Calculator

The hydrogenic radius scales as n squared over the effective nuclear charge, with the Bohr radius (52.92 pm) setting the scale. Slater's rules give the effective charge as Z minus a shielding constant. Sodium, with n = 3, Z = 11 and S near 8.8, comes out around 215 pm - which explains both trends at once: radius grows down a group as n rises, and shrinks across a period as effective charge rises faster than shielding.

Formulas

Effective nuclear charge

Zeff = Z - S

Hydrogenic radius

r = n^2 x a0 / Zeff, with a0 = 52.9177 pm

Worked example

With the default values below, Atomic Radius Trend Calculator returns Estimated Atomic Radius of 216.5. Change any input above and every figure here is recalculated in your browser.

Inputs used

Principal quantum number of the outer shell (n)accepts 1–7
3
Atomic number Zminimum 1
11
Slater shielding constant Sminimum 0
8.8

Results

Estimated Atomic Radius
216.5 pm
Effective Nuclear Charge
2.200
Same Radius In Angstrom
2.165
Share Of Nuclear Charge Screened
80.00%

Step by step

  1. 1Values used
  2. 2Effective nuclear charge
  3. 3Hydrogenic radius
  4. 4Estimated Atomic Radius= 216.5 pm
  5. 5Effective Nuclear Charge= 2.200
  6. 6Same Radius In Angstrom= 2.165
  7. 7Share Of Nuclear Charge Screened= 80.00

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does radius shrink across a period?

Each added proton pulls harder, but the added electron shields only partly, so effective charge rises and the shell contracts.

How accurate is the Slater estimate?

It captures the trends but not the absolute values, typically within 20-30% of measured covalent radii. Use it for comparison, not for bond lengths.

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