RREF Calculator (Reduced Row Echelon Form)
A matrix is in reduced row echelon form when every nonzero row starts with a leading 1, each leading 1 is the only nonzero entry in its column, and leading 1s move right as you go down.
At a glance
| What it is | Free RREF calculator: reduce any matrix to reduced row echelon form with exact fractions. Find rank and solve linear systems. No sign-up. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Leading entries | Every nonzero row starts with a 1 |
|---|---|
| Pivot columns | All other entries are 0 |
| Order | Each leading 1 is to the right of the one above; zero rows at the bottom |
| Rank | Number of nonzero rows in the RREF |
| Example | rref([[1, 2, 3], [2, 5, 8]]) = [[1, 0, −1], [0, 1, 2]] |
How do you solve a system with RREF?
Write a system as an augmented matrix, with the coefficients followed by the constants, and reduce it. In the example, [[1, 2, 3], [2, 5, 8]] stands for x + 2y = 3 and 2x + 5y = 8, and the RREF reads x = −1, y = 2.
How to use it in Plotline
- Matrix A is filled in with an example and rref(A) is calculated.
- Enter your own matrix (augmented matrices are fine) and type rref(A).
- Use rank(A) to count independent rows.
Frequently asked questions
What is the difference between REF and RREF?
Row echelon form (REF) only needs zeros below each pivot. Reduced row echelon form also needs zeros above each pivot, and every pivot equal to 1. RREF is unique for each matrix.
Is it free?
Yes. The matrix calculator is free with no account and no sign-up, and there is no limit on how many matrices you work with. Determinants, inverses, RREF, multiplication and systems of equations are all included, and it works offline once loaded.
Learn more
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.