These 2 drawings refer to the same single rhombus.
a = side lengths
p and q diagonal lengths
h = height
A, B, C, D = corner angles
K = area
P = perimeter
π = pi = 3.14159
√ = square root
Calculate certain variables of a rhombus depending on the inputs provided. Calculations include side lengths, corner angles, diagonals, height, perimeter and area of a rhombus.
A rhombus is a quadrilateral with opposite sides parallel and all sides equal length. A rhombus whose angles are all right angles is called a square. A rhombus (or diamond) is a parallelogram with all 4 sides equal length.
* Units: Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the calculated results such as ft, ft2 or ft3. Any other base unit can be substituted.
Corner Angles: A, B, C, D
- A = C
- B = D
- A + B = 180° = π radians
- for a rhombus that is not a square,
- 0 < A< 90° (0 < A < π/2)
- 90° < B < 180° (π/2 < B < π)
with A and B in radians,
K = ah = a2 sin(A) = a2 sin(B) = pq/2
- h = ha = hb
- h = a sin(A) = a sin(B)
Diagonals: p, q
- p = a √( 2 - 2 cos(A) ) = a √( 2 + 2 cos(B) )
- q = a √( 2 + 2 cos(A) ) = a √( 2 - 2 cos(B) )
- p2 + q2 = 4a2
P = 4a
The following formulas, based on those above, are used within this calculator for the selected calculation choices.
Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 323, 2003.
Math Forum: Ask Dr. Math FAQ: Quadrilateral Formulas (http://mathforum.org/)