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A sodium atom has eleven protons, but its outer electron does not behave as though it were attracted by an unscreened charge of +11. Other electrons screen part of the nuclear attraction. Slater’s rules turn that idea into an approximate calculation for a chosen electron.
Choose the electron before calculating
Effective nuclear charge in this model is Zeff = Z − S. Z is the atomic number, and S is a screening constant built from the other occupied subshells. Different electrons in the same atom generally have different screening constants.
The Effective Nuclear Charge Calculator starts with a neutral ground-state configuration, lets you select an occupied subshell, and displays the contribution from each relevant subshell. Its supported range is H through U. Ion configurations are outside this version.
The ns and np rules
For an ns or np electron, group ns and np together. Each other electron in that group contributes 0.35 to S, except that the other electron in 1s contributes 0.30. Electrons with principal quantum number n − 1 contribute 0.85 each; electrons in still lower shells contribute 1.00 each. Electrons outside the relevant groups do not contribute in this rule set.
For sodium's 3s electron, the eight electrons in the second shell contribute 8 × 0.85 = 6.80. The two 1s electrons contribute 2 × 1.00 = 2.00. There are no other 3s/3p electrons. Thus S = 8.80 and Zeff = 11 − 8.80 = 2.20.
The nd and nf rules
For a d or f electron, the grouping changes. Other electrons in the same nd or nf subshell contribute 0.35 each. Electrons in groups to its left contribute 1.00 each. Outer groups contribute zero. This is why applying the ns/np formula indiscriminately to d electrons gives the wrong result.
For an iron 3d electron in the usual neutral configuration, the other five 3d electrons contribute 1.75. The eighteen electrons in the inner groups contribute 18.00, giving S = 19.75 and Zeff = 6.25. The 4s electrons do not screen that 3d electron under these rules.
What the estimate means
Slater’s rules are an empirical screening model. Their output is neither the atom's net ionic charge nor a measured oxidation state. More detailed quantum calculations can use different definitions and yield different screening values.
Check the underlying occupancy with the Electron Configuration Calculator. Its guide to filling rules and exceptions covers configurations such as chromium and copper that a simple diagonal filling pattern misses. Return to the Chemistry category for related structure and bonding tools.
By GreenCalc · Updated 2026-10-21
Frequently asked questions
Is effective nuclear charge the ionic charge?
No. Slater effective charge describes a selected electron in an approximate screening model.
Which atoms are supported?
Neutral ground-state atoms with atomic numbers 1 through 92, hydrogen to uranium.