Effective Nuclear Charge Calculator
Estimate the nuclear attraction experienced by a selected electron using Slater’s shielding rules, or subtract a known shielding constant from Z.
01 Set up your calculation
- Enter the atomic number, which counts protons. Choose Slater’s rules to estimate S, or enter a known shielding constant directly.
- For Slater’s rules, provide occupied subshells with explicit counts, separated by spaces or commas: 1s2 2s2 2p6, 1s^2 2s^2 2p^6, and superscript counts are accepted. You may begin with one noble-gas core such as [Ne].
- Select an occupied target subshell. Read Zeff, S and the contributions; all charge numbers and shielding values are dimensionless. For ions, check that the implied ion charge matches your intended species.
02 The relationship
For the assumptions behind these results, read the explanation below. You can also explore Atom and Electronegativity.
Follow the numbers
For a chlorine 3p electron, six other electrons share the (3s, 3p) group, eight occupy n = 2, and two occupy n = 1. S = 6 × 0.35 + 8 × 0.85 + 2 × 1.00 = 10.90. With Z = 17, Zeff = 6.10.
03 Choose an electron before choosing a shielding value
Zeff describes a selected electron’s approximate nuclear attraction after screening by the other electrons. It is not the net charge of the whole atom. Hydrogen with one electron has S = 0; in a larger atom, core and outer electrons generally have different estimates.
The results use charge numbers, not coulombs. The separate ion charge number is Z minus the total electron count. A neutral chlorine configuration therefore has ion charge zero even when its 3p effective nuclear charge is 6.10.
04 Keep Slater groups separate from filling order
The screening groups run (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f), and onward by principal shell. The s and p subshells of a shell are grouped together; d and f are separate. The selected electron never screens itself.
For example, enter iron as [Ar] 3d6 4s2. A 3d target receives 18 × 1.00 from earlier groups and 5 × 0.35 from the other 3d electrons: S = 19.75 and Zeff = 6.25. Its two 4s electrons contribute zero under these rules. Choosing 4s instead gives S = 22.25 and Zeff = 3.75.
05 Supply the configuration for the actual species
Use the electron arrangement of the atom or ion you mean. The calculator expands [He], [Ne], [Ar], [Kr], [Xe] and [Rn], then checks subshell capacities. It accepts occupied s, p, d and f subshells with n from 1 to 7 and totals from 1 to 118 electrons. Omit empty subshells and do not repeat any already included in a noble-gas core.
No ground-state arrangement is guessed from Z. This matters for exceptions such as chromium and copper, and for transition-metal ions whose outer s electrons are removed before d electrons. Changing the written order of valid subshells does not change the answer.
06 Use the result as a screening estimate
Slater’s fixed weights simplify electron distributions into a few counts. They help compare screening, but do not replace measured ionization energies or a detailed quantum calculation. Equal estimates for ns and np electrons are a feature of this grouping approximation.
The tool checks notation, electron capacities and a positive Zeff; it does not establish that an entered configuration is a stable or ground-state species. Manual mode assumes your S applies to the electron of interest and requires 0 ≤ S < Z. It cannot assess the quality of that supplied shielding constant.
Questions from the notebook
Do I subtract the electron I am studying?
Yes. It is excluded from its own group before the shielding contribution is calculated. Helium 1s2 has only one other 1s electron, so S = 0.30 and Zeff = 1.70.
Does a 3d electron screen a 4s electron by 0.85 or 1.00?
This implementation uses 0.85 for every electron in the n − 1 shell of an s or p target, including d electrons in that shell. The separate 1.00 rule for earlier groups applies when the target itself is d or f.
Can I calculate an ion?
Yes. Keep Z unchanged and enter the ion’s electron configuration. The displayed Z minus electron count identifies the implied ion charge number. For Na+ with Z = 11 and configuration [Ne], a 2p target gives Zeff = 6.85.
Can I enter a noble-gas core by itself?
Yes. For example, [Ne] expands to 1s2 2s2 2p6. Choose a target present in that core. An extra 2p entry would duplicate electrons and is rejected.
Is this the same as subtracting all core electrons from Z?
No. Slater’s method weights the shielding according to the selected group and includes contributions from other electrons in that group. Counting every core electron as exactly one is a different approximation.
References & reading
- University of Wisconsin–Madison — Slater Shielding Constant ↗
Defines the Slater grouping sequence, 0.30/0.35/0.85/1.00 shielding weights, and the distinct s/p and d/f rules.
- Graz University of Technology — Slater’s Rules ↗
The written rules clarify same-group screening and earlier groups for d/f targets. The calculator implements those rules; it does not use the page’s numerical table.
- OpenStax, Rice University — Chemistry 2e: Electronic Structure of Atoms ↗
Supports electron-configuration notation, noble-gas shorthand, subshell capacities, filling exceptions and the removal of electrons when ions form.
- OpenStax, Rice University — Chemistry 2e: Periodic Variations in Element Properties ↗
Explains effective nuclear charge as Z minus shielding and relates screening to periodic trends. This chapter supplies context rather than Slater’s numerical weights.
Our explanations are written for ChemistryCalc. Read how we build and check our tools. These calculations are educational estimates where the underlying model requires assumptions.