Effective Nuclear Charge Calculator
Enter the atomic number Z and a shielding constant S (for example, one estimated using Slater's rules from a chemistry reference) to find the effective nuclear charge Zeff felt by an electron.
Last updated: September 26, 2026
Frequently asked questions
What is effective nuclear charge?
It's the net positive charge an electron actually experiences from the nucleus, after accounting for the shielding (screening) effect of other electrons. It's always less than the full nuclear charge Z, except for a single electron with no other electrons to shield it.
Does this calculator estimate the shielding constant for me?
No. You supply Z and S directly; the calculator only computes Zeff = Z − S. A common method to estimate S, Slater's rules, requires knowing which specific electron and subshell you're evaluating, and different textbooks present slightly different rule sets.
Is effective nuclear charge the same as ionic charge?
No. Ionic charge describes the overall charge of an ion after gaining or losing electrons. Effective nuclear charge describes how strongly a specific electron in a specific atom or ion is attracted to the nucleus, accounting for shielding by other electrons.
Why can't the shielding constant exceed the atomic number?
If S were greater than Z, the effective nuclear charge would be negative, implying the electron is net repelled rather than attracted by the nucleus, which isn't a physically meaningful result in this model.
Why does Zeff generally increase across a period?
Moving across a period, protons are added to the nucleus faster than effective shielding increases (since added electrons go into the same outer shell and shield each other only partially), so Zeff on outer electrons tends to increase left to right.
How does this relate to Electron Configuration?
Electron configuration tells you which subshell an electron occupies, which is exactly the information you need to look up or estimate a shielding constant (for example with Slater's rules) before using this calculator.