Parallelogram area (with sine)

Type sides a, b and the angle in degrees. P = a×b×sin(c°). 4, 5 and 30° give 10.000000. 3, 4 and 90° give 12. 2, 2 and 60° give 3.464102.

The angle is in degrees, not radians. 4, 5 and 30° show 10.000000, not a clean 10, because sin(30×π/180) is not exactly 1/2.

Input data

Results

Enter data and click Calculate.

How it works

Parallelogram area with sine multiplies two sides and the sine of the angle between them. The calculator calls a*b*Math.sin(c*π/180). 3, 4 and 90° give 12, a clean string, because sin 90° comes out 1.

4, 5 and 30° in a notebook are 10. Here sin(30×π/180) leaves 0.49999999999999994, the product 9.999999999999998, and six decimal places writes 10.000000. That is not an integer String.

2, 2 and 60° give 3.464102, 2√3 after six decimal places. 0° leaves 0. An empty field is a blank value and a blank. A minus angle gives a minus area.

The calculator with base and height is on the neighbouring page. There a×h, no sine. Sine of an angle in degrees lives on the sine page. We do not overwrite that page.

The header units switch does not multiply anything. 3, 4 and 90 stay 12 whatever the label says.

4, 5 and 30° give 10.000000. 3, 4 and 90° give 12. 2, 2 and 60° give 3.464102.

Formula

P = a × b × sin(c°)

How to use

  1. Type the sides, for example 4 and 5, and the angle in degrees, for example 30.
  2. Click Calculate. The area comes out 10.000000, not a clean 10.
  3. 3, 4 and 90° give 12. 2, 2 and 60° give 3.464102.
  4. The angle is in degrees. 30 means 30°, not 30 radians.
  5. Area from base and height lives on the neighbouring card.

4, 5 and 30° give 10.000000

P = a×b×sin(c°). 4, 5 and 30° give 10.000000. 3, 4 and 90° give 12. 2, 2 and 60° give 3.464102.

Parallelogram
Two sides and an angle. 3, 4 and 90° give 12. 4, 5 and 30° give 10.000000.
sine
Math.sin(c×π/180). 30° does not give a clean 10. 60° with 2 and 2 gives 3.464102.
area
The product a×b×sin(c°). An integer result goes as a string. A fraction as six decimal places.

Examples

Example 1

  • a = 4
  • b = 5
  • α = 30°

10.000000

What is the area at 4, 5 and 30°? 10.000000. machine float and six decimal places, not a clean 10.

Example 2

  • a = 3
  • b = 4
  • α = 90°

12

What is the area at 3, 4 and 90°? 12. sin 90° = 1, an integer string.

Example 3

  • a = 2
  • b = 2
  • α = 60°

3.464102

What is the area at 2, 2 and 60°? 3.464102. That is 2√3 after six decimal places.

Related calculators

Parallelogram area calculator

Parallelogram area calculator: the base and the height perpendicular to it.

Use calculator →

Sine of an angle calculator

Pick from an angle or from triangle sides (sine angle).

Use calculator →

All mathematics calculators

Common questions

What is the area at 4, 5 and 30°?

10.000000. In a notebook, 10. Here 9.999999999999998 and six decimal places.

What does parallelogram area with sine mean?

Two sides and the angle between them. a×b×sin(c°). Angle in degrees.

What about 3, 4 and 90°?

12. A 3 by 4 rectangle. An integer result, no six zeros.

What about 2, 2 and 60°?

3.464102. 2√3 after six decimal places.

Is the angle in radians?

No. The engine multiplies c by π/180. 30 means 30°.

Why not a clean 10?

sin(30×π/180) is not exactly 0.5. Generic does not promote that to an integer String.

What if a field is empty?

a blank value. The result stays blank.

Does 0° give 0?

Yes. sin 0° = 0, area 0.

Where is area from a height?

On the parallelogram area card. There a×h.

Does a comma in 30.5 work?

Yes. 30.5 and 30,5 are the same angle.

Knowledge sources

The calculator computes the same formula as the definition below.

Page updated in 2026.