Rhombus Calculator — Area, Perimeter, Diagonals and Angles

Enter a side and angle, both diagonals, or a side and one diagonal to calculate the rhombus’s complete geometry.

Enter rhombus measurements

Known measurements

Enter any one interior angle. The calculator also finds its supplementary angle.

Side length s

The shared length of all four sides

Interior angle θ

Greater than 0° and less than 180°

Unit for lengths

Decimal places Choose 0 to 10

Use one unit: enter every length in the selected unit. Changing the selector changes labels only; it does not convert entered values. Area is shown in square units.

Rhombus results

Enter valid measurements and select Calculate to see area, perimeter, side, diagonals, angles, height, inradius and calculation steps.

Rhombus formulas

Let s be the side length, p and q the diagonals, θ an interior angle, h the perpendicular height, and r the inradius.

Area

A = pq/2 = s² sin θ = sh

Choose the form that matches the measurements you know.

Perimeter

P = 4s

Every side has the same length, so the perimeter is four sides.

Side from diagonals

s = ½√(p² + q²)

The half-diagonals are perpendicular legs of a right triangle.

Diagonals from side and angle

p = 2s cos(θ/2)
q = 2s sin(θ/2)

The diagonal labels exchange when the supplementary angle is used.

Angles from diagonals

α = 2 tan⁻¹(short/long)
β = 180° − α

A rhombus has two equal acute angles and two equal obtuse angles.

Height and inradius

h = A/s
r = A/(2s) = h/2

The incircle’s diameter equals the perpendicular height.

Diagonal rule: a rhombus’s diagonals bisect each other at right angles. They are not generally equal; equal diagonals make the rhombus a square.

Worked examples

Side and 60° angle

For s = 6 cm and θ = 60°, area is 31.18 cm², perimeter is 24 cm, and the diagonals are 6 cm and 10.39 cm.

Both diagonals

For p = 16 m and q = 12 m, area is 96 m², the side is 10 m, and the perimeter is 40 m.

Square special case

For side s = 5 in and diagonal d = 7.0711 in, the other diagonal is also about 7.0711 in and the angles are 90°.

Method, precision and privacy

Method:
Euclidean geometry, right triangles and trigonometry

Numerical policy:
Full browser precision is used until display rounding

Input limits:
Positive finite lengths up to 10¹⁵⁰; angles strictly between 0° and 180°

Last reviewed:
30 July 2026

All values stay in your browser. The calculator does not send, save or include your measurements in analytics. Extremely narrow rhombuses are mathematically valid, but very small results may display in scientific notation or round to zero at low precision.

Rhombus calculator FAQs

How do you find the area of a rhombus?

Multiply the diagonals and divide by two: A = pq/2. With side s and interior angle θ, use A = s² sin θ. You can also multiply a side by the perpendicular height.

How do you find the perimeter of a rhombus?

Multiply the side length by four: P = 4s. All four sides of a rhombus have equal length.

How do you find a rhombus side from its diagonals?

The half-diagonals form a right triangle, so s = ½√(p² + q²).

How do you find the angles of a rhombus from its diagonals?

If q is the shorter diagonal and p is the longer diagonal, the acute angle is 2 tan⁻¹(q/p). The obtuse angle is 180° minus the acute angle.

Are the diagonals of a rhombus equal?

Not usually. Rhombus diagonals bisect each other at right angles, but they are equal only in the square special case.

Can a side and one diagonal make a rhombus?

Yes, provided the diagonal is positive and shorter than twice the side. The other diagonal is √(4s² − d²).

Is every square a rhombus?

Yes. A square has four equal sides, so it is a rhombus whose four angles are 90° and whose diagonals are equal.