---
title: "Zernike RMS Wavefront Error calculator — AperiOptic"
description: "RMS WFE from a list of normalized Zernike coefficients (waves). Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/zernike-rms-wavefront-error"
---

# Zernike RMS Wavefront Error calculator

RMS WFE from a list of normalized Zernike coefficients (waves).

Category: [Aberrations](https://aperioptic.com/calculators)

Formula: `WFE_rms = √Σ cᵢ²`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Defocus c | `c1` | λ | 0.05 |
| Astig c | `c2` | λ | 0.03 |
| Coma c | `c3` | λ | 0.04 |
| Spherical c | `c4` | λ | 0.02 |

## Result with the default inputs

- RMS WFE: 0.0735 λ
- PV (~5×): 0.3674 λ

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/zernike-rms-wavefront-error?c1=0.05`](https://aperioptic.com/calculators/zernike-rms-wavefront-error?c1=0.05). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Zernike polynomials](https://en.wikipedia.org/wiki/Zernike_polynomials)

[All optics calculators](https://aperioptic.com/calculators)

---

The interactive page: https://aperioptic.com/calculators/zernike-rms-wavefront-error (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt