Chemistry

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Effective Nuclear Charge Calculator.

Calculate effective nuclear charge from nuclear charge and an explicit shielding constant.

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Set your values

Results update as you type.

Effective charge: 2.2 e

Effective charge

2.20e

How to Use

Zeff = Z − σ. The shielding constant is intentionally entered by you; no orbital or element table is hidden.

Use a named source for any material-specific coefficient. This page does not infer local rates, species tables, laboratory methods, or safety guidance.

Use Cases

Chemistry homework and exam prep

Quickly compute effective nuclear charge for atoms or ions when you have Z and σ values, helping you understand periodic trends like atomic radius and ionization energy.

Example: For sodium (Z=11) with σ=10, Zeff = 1.

Research and teaching demonstrations

Use the calculator to illustrate how electron shielding affects the net attraction between the nucleus and outer electrons in lectures or lab reports.

Example: Show how Zeff increases across a period as Z increases while σ changes.

Frequently Asked Questions

What is effective nuclear charge?
Effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It equals the nuclear charge (Z) minus the shielding constant (σ), which accounts for repulsion by inner electrons. This calculator computes Zeff = Z - σ.
How do I use this calculator?
Enter the nuclear charge (Z) in units of e (elementary charge) and the shielding constant (σ) in the same units. The calculator subtracts σ from Z to give the effective nuclear charge. For example, for lithium (Z=3) with σ=2, Zeff = 1.
What is the shielding constant?
The shielding constant (σ) represents the amount of nuclear charge that is 'shielded' or canceled by inner electrons. It is often estimated using Slater's rules or other models. This calculator requires you to input σ explicitly, as it does not compute it automatically.

Tips & Common Mistakes

Tips

  • Ensure both Z and σ are in the same unit (e) to get Zeff in e. The calculator does not convert units.
  • For a neutral atom, Z equals the number of protons. For ions, adjust Z accordingly (e.g., for Fe³⁺, Z=26).
  • If you don't have σ, you can estimate it using Slater's rules, but this calculator requires an explicit value.
  • Remember that Zeff is always less than or equal to Z, since σ is non-negative.

Common Mistakes to Avoid

  • Entering σ as a percentage or fraction instead of a plain number in e. For example, use 2, not 0.2 or 20%.
  • Confusing nuclear charge (Z) with atomic number for ions. For ions, Z is still the number of protons, not the number of electrons.
  • Forgetting that σ must be less than or equal to Z; otherwise, Zeff would be negative, which is physically unrealistic.

Last updated: August 13, 2026