What is effective nuclear charge?

Effective nuclear charge (Zeff) is the net positive charge experienced by a specific electron after accounting for the shielding effect of all other electrons. It equals the atomic number Z minus the shielding constant S.

What are Slater's rules?

Slater's rules are an empirical set of guidelines that estimate the shielding constant S. Electrons are grouped as [1s] [2s,2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s,5p] … and each group contributes a fixed fraction to shielding based on its position relative to the target electron.

How accurate is this calculation?

Slater's rules give a useful approximation but not exact quantum-mechanical values. For high-precision work, self-consistent field (SCF) calculations are needed. Slater's Zeff values are widely used in introductory and intermediate chemistry.

Why does Zeff increase across a period?

Across a period, Z increases by 1 for each element but the added electron goes into the same shell, contributing only about 0.35 to shielding. The net effect is that Zeff rises, pulling electrons closer and reducing atomic radius.

What shielding value is used for inner-shell electrons?

For an electron in an s or p orbital, electrons in groups below (inner shells) each contribute 1.00 to S, electrons in the same group contribute 0.35 each (except 1s, which uses 0.30), and electrons in the next lower shell (n−1) contribute 0.85 each.

Effective Nuclear Charge Calculator

Name: Effective Nuclear Charge Calculator
Availability: InStock
Author: Nham Vu

Enter an element and electron shell to calculate Zeff using Slater's rules with a full shielding breakdown.

Element & Shell

Element symbol or atomic number

Target electron group

Quick pick

Enter an element and click Calculate to see the Zeff breakdown.

Effective Nuclear Charge

Z_eff

Atomic Number (Z)

Shielding (S)

Z − S

Shielding Breakdown (Slater Groups)

Group	Electrons	Per e⁻	Contribution
Total shielding (S)

Target group: . Electrons in the target group (excluding the target electron itself) contribute 0.35 each (0.30 for 1s).

Electron Configuration

Summary

Enter an element and electron shell to calculate Zeff using Slater's rules with a full shielding breakdown.

How it works

Select an element from the periodic table or enter an atomic number (1–118).
Choose the target electron shell (n = 1 through the valence shell).
The tool groups electrons according to Slater's rules.
Each group's shielding contribution is summed to give the total shielding constant (S).
Zeff = Z − S is displayed along with the per-group breakdown.

Use cases

Predict atomic radius trends across periods and groups.
Understand why ionization energy increases across a period.
Compare electronegativity differences between elements.
Support general chemistry and quantum chemistry coursework.
Verify hand-calculated Slater shielding results.
Explore how electron configuration affects nuclear attraction.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu