---
title: "RREF Calculator — Reduced Row Echelon Form, Rank & Nullity"
description: "Compute the Reduced Row Echelon Form (RREF) of any matrix (up to 5×6). Shows every row operation, finds rank, nullity, and pivot columns. Used in linear systems, basis, and null space."
url: "https://worldcalculators.org/calculators/rref/"
canonical: "https://worldcalculators.org/calculators/rref/"
---

# RREF Calculator

Compute the Reduced Row Echelon Form (RREF) of any matrix (up to 5×6). Shows every row operation, finds rank, nullity, and pivot columns. Used in linear systems, basis, and null space.

## Quick answer

Matrix ( 3 × 4 )

## Frequently Asked Questions

Row Echelon Form (REF) requires pivots below to be zero, but doesn't require pivots to equal 1 or eliminate entries above. RREF (Reduced REF) goes further: all pivots are exactly 1, and all other entries in pivot columns are 0. RREF is unique; REF is not. Gauss elimination gives REF; Gauss-Jordan gives RREF. Both have the same pivot columns and rank.
Yes — RREF works on any m×n matrix, not just square ones. A 3×5 matrix in RREF might have 2 pivot rows and 3 free columns. This is one of its most important uses: analyzing underdetermined systems (more unknowns than equations) to find all solutions, or overdetermined systems (more equations than unknowns) to check consistency.

Source: https://worldcalculators.org/calculators/rref/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.