How do you find the perimeter of a parallelogram?

Add the two adjacent side lengths and double the result: P = 2(a + b). Height and angle are not needed for perimeter.

How do you find the diagonals of a parallelogram?

For adjacent sides a and b and included angle θ, the diagonals are √(a² + b² + 2ab cos θ) and √(a² + b² − 2ab cos θ).

Can base and height determine every parallelogram measurement?

No. Base and perpendicular height determine area, but not the adjacent side, perimeter or diagonals. This calculator’s height mode also requires the adjacent side length.

Why must the height be no greater than the adjacent side?

The height relative to base a is h = b sin θ. Since sin θ cannot exceed 1, h cannot exceed side b. Equality occurs when the included angle is 90°.

Why can the same base, side and height give two angles?

An acute angle θ and its supplement 180° − θ have the same sine, so they produce the same height and area. The two diagonal lengths are also the same pair, but their labels swap.

Parallelogram Calculator — Area, Perimeter, Height and Diagonals

Enter two adjacent sides and their included angle—or a base, adjacent side and perpendicular height—to calculate the parallelogram’s complete geometry.

Enter parallelogram measurements

Known measurements

Use the interior angle where side a meets side b. Angles are entered in degrees.

Side a (base)

A positive base length

Side b (adjacent side)

The side next to base a

Included angle θ

Greater than 0° and less than 180°

Unit for all lengths

Decimal places Choose 0 to 10

Use one unit: enter both sides and height, when used, in the selected unit. Changing the selector changes labels only; it does not convert entered values. Area is shown in square units.

Parallelogram results

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

Parallelogram formulas

Let a and b be adjacent sides, θ their included angle, h_a the perpendicular height to base a, h_b the height to base b, and d₁ and d₂ the diagonals.

Area

A = ah_a = ab sin θ

A base times its perpendicular height. Square the selected length unit.

Perimeter

P = 2(a + b)

Opposite sides are equal, so each adjacent side occurs twice.

Heights

h_a = b sin θ
h_b = a sin θ

Each height depends on which side is chosen as the base.

Diagonal 1

d₁ = √(a² + b² + 2ab cos θ)

This is the vector-sum diagonal for the entered angle.

Diagonal 2

d₂ = √(a² + b² − 2ab cos θ)

This is the vector-difference diagonal. The two diagonals bisect each other.

Angle from height

θ = sin⁻¹(h_a/b)

The supplementary angle 180° − θ has the same height and area.

Determination rule: base and height alone do not determine a unique parallelogram. The adjacent side or equivalent extra information is needed to find the perimeter and diagonals.

Worked examples

Two sides and a 60° angle

For a = 8 cm, b = 5 cm and θ = 60°, area is 34.64 cm², perimeter is 26 cm, and height to base a is 4.33 cm.

Base, side and height

For a = 10 m, b = 6 m and h_a = 3 m, area is 30 m². The principal angle is 30°, with a 150° supplementary solution.

Rectangle special case

For a = 12 in, b = 5 in and θ = 90°, both diagonals are 13 in, area is 60 in², and perimeter is 34 in.

Method, precision and privacy

Method:
Euclidean geometry, trigonometry and the law of cosines

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:
29 July 2026

All values stay in your browser. The calculator does not send, save or include your measurements in analytics. Very thin parallelograms near 0° or 180° are mathematically valid, but displayed values may round to zero at low precision.

Parallelogram calculator FAQs

How do you find the area of a parallelogram?

Multiply a base by its perpendicular height: A = ah. With adjacent sides a and b and their included angle θ, use A = ab sin θ.

How do you find the perimeter?

Add the adjacent sides and double the result: P = 2(a + b). The angle and height do not affect perimeter.

How are the two diagonals calculated?

Use d₁ = √(a² + b² + 2ab cos θ) and d₂ = √(a² + b² − 2ab cos θ). At 90°, the diagonals are equal because the parallelogram is a rectangle.

Can base and height determine all the other values?

No. They determine area, but many parallelograms can share that base and height. An adjacent side or equivalent information is needed for perimeter and diagonals.

Why must height be no greater than side b?

Because h_a = b sin θ and sine cannot exceed 1. If height equals side b, the included angle is 90°.

Why does height mode show two possible angles?

An acute angle and its supplementary obtuse angle have the same sine. They therefore produce the same area and heights; the two diagonal lengths remain the same pair but exchange labels.