Rectangle Calculator: Area, Perimeter & Diagonal

An easy to use online calculator to calculate the area, perimeter, and diagonal of a rectangle is presented. The calculator has two modes:

Mode 1: Given the length \( L \) and width \( W \), compute the area \( A \), perimeter \( P \), and diagonal \( D \).
Mode 2: Given the area \( A \) and perimeter \( P \), compute the length \( L \), width \( W \), and diagonal \( D \).

The formulas for the perimeter \( P \), area \( A \) and length \( D \) of the diagonal of a rectangle of length \( L \) and width \( W \) are given by:

Rectangle with length L, width W and diagonal D — *Figure 1. Rectangle with length \(L \), width \( W \) and diagonal \( D \)*

\[ P = 2L + 2W \] \[ A = L \times W \] \[ D = \sqrt{L^2 + W^2} \]

When the area \( A \) and perimeter \( P \) are known, the length and width are obtained by solving the system of first two equations above, which leads to the quadratic equation:

\[ x^2 - \frac{P}{2}x + A = 0 \]

The length \( L \) and width \( W \) are the two roots of this equation:

\[ L = \frac{\frac{P}{2} + \sqrt{\left(\frac{P}{2}\right)^2 - 4A}}{2} \] \[ W = \frac{\frac{P}{2} - \sqrt{\left(\frac{P}{2}\right)^2 - 4A}}{2} \]

Note: For a valid rectangle, the condition \( P^2 \geq 16A \) must be satisfied. If \( P^2 < 16A \), no real rectangle exists with the given area and perimeter.

💡 Two Ways to Use:

Mode 1 (L,W → A,P,D): Enter Length and Width to find Area, Perimeter, and Diagonal
Mode 2 (A,P → L,W,D): Enter Area and Perimeter to find Length, Width, and Diagonal

Rectangle Calculator

Choose input mode below

Find Area, Perimeter & Diagonal from Dimensions

Length (L)

Width (W)

Find Length, Width & Diagonal from Area and Perimeter

Area (A)

Perimeter (P)

Decimal Places

Area (A) -- sq units

Perimeter (P) -- units

Diagonal (D) -- units

Length (L) -- units

Width (W) -- units

Diagonal (D) -- units

Rectangle Calculator: Area, Perimeter & Diagonal

Rectangle Calculator

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