Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

Rectangle calculator

Select the missing value after entering two rectangle elements (length, width, diagonal, area, or perimeter). The calculator will provide you a step-by-step solution to the given problem.
show help ↓↓ examples ↓↓ tutorial ↓↓
Input what to find:
Input any two known values of a rectangle
calculator works with decimals, fractions and square roots ( to input $ \color{blue}{\sqrt{2}} $ type $ \color{blue}{\text{r2}} $)
side
$ a $ =
 
side
$ b $ =
diagonal
$ d $ =
 
area
$ A $ =
perimeter
$ P $ =
 
working...
Rectangle formulas
$$ A = ab $$
area
$$ P = 2a + 2b $$
perimeter
$$ d^2 = a^2 + b^2 $$
diagonal
EXAMPLE PROBLEMS
example 1:ex 1:
Find the area of the rectangle whose sides are $ a = \dfrac{5}{3} $ and $ b = \dfrac{3}{2} $.
example 2:ex 2:
If the diagonal is 9 cm and one side is 5 cm, find the area of a rectangle.
example 3:ex 3:
A rectangle has an area of 18 cm2 and a side length of 16/5cm. Determine the perimeter.
Search our database of more than 200 calculators
TUTORIAL

Rectangle calculations

This calculator uses the following formulas to find the missing values of a rectangle:

Area: $$ A = a \cdot b $$ rectangle
Perimeter: $$ P = 2a + 2b $$
Diagonal: $$ d^2 = a^2 + b^2 $$

Example 01 :

What is the area of a rectangle with a base of 12 cm and a height of 3/2 cm?

Solution:

base $ a = 6 $

height $ b = \dfrac{9}{2} $

$$ \color{blue}{A = a \cdot b} = 6 \cdot \frac{9}{2} = \frac{54}{2} = 27 $$

Example 02 :

What is the perimeter of a rectangle with a length of 7/2cm and a width of 5/2cm?

Solution:

length $ a = \dfrac{7}{2} \, cm $

width $ b = \dfrac{5}{2} \, cm $

$$ \color{blue}{P = 2a + 2b} = 2 \cdot \frac{7}{2} + 2 \cdot \dfrac{5}{2} = 7 + 5 = 12 $$

Example 03 :

The area of a rectangle is 42 cm2. Find its perimeter if the width is 7cm.

Solution:

We'll need two steps to solve this one:

Step 1: find length ( b ):

width $ a = 7 cm $

area: $ A = 42 cm $

$$ \begin{aligned} A & = a \cdot b \\[ 1 em] 42 & = 7 \cdot b \\[ 1 em] b & = \frac{42}{7}\\[ 1 em] b & = 6 \\[ 1 em] \end{aligned} $$

Step 2: find perimeter ( P )

width $ a = 7 cm $

length $ b = 6 cm $

$$ \begin{aligned} P & = 2a + 2b \\[ 1 em] P & = 2 \cdot 7 + 2 \cdot 6 \\[ 1 em] P & = 14 + 12 \\[ 1 em] P & = 28 \, cm^2 \\[ 1 em] \end{aligned} $$

Example 04 :

What is the diagonal of a rectangle if the perimeter is P = 11/2 cm and a width is a = 3/2 cm ?

Solution:

Step 1: find length ( b ):

width $ a = \dfrac{3}{2} cm $

perimeter: $ P = \dfrac{11}{2} cm $

$$ \begin{aligned} P & = 2a + 2b \\[ 1 em] \frac{11}{2} & = 2 \cdot \frac{3}{2} + 2b \\[ 1 em] \frac{11}{2} & = 3 + 2b \\[ 1 em] 2b &= \frac{11}{2} - 3 \\[1 em] 2b &= \frac{5}{2} \\[1 em] b &= \frac{5}{4} \end{aligned} $$

Step 2: find diagonal ( d )

width $ a = \dfrac{3}{2} cm $

length $ b = \dfrac{5}{4} cm $

$$ \begin{aligned} d^2 & = a^2 + b^2 \\[ 1 em] d^2 & = \left( \frac{3}{2} \right)^2 + \left( \frac{5}{4} \right)^2 \\[ 1 em] d^2 & = \frac{9}{4} + \frac{25}{16} \\[ 1 em] d^2 & = \frac{61}{16} \\[ 1 em] d & = \frac{\sqrt{61}}{4} \end{aligned} $$
Search our database of more than 200 calculators

Was this calculator helpful?

Yes No
437 783 523 solved problems