Rhombus Calculator

Rhombus
Choose a Calculation:
a = m
h = m

Units*:
Significant Figures:

Answer:

A = C =
B = D =
a =
p =
q =
h =
P =
K =

Rhombus Shapes

rhombus diamond shape labeled with angles, sides and diagonals rhombus shape labeled with angles, side and height
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

Rhombus Calculator

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.

Rhombus Formulas & Constraints

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)

Area: K

with A and B in radians,

K = ah = a2 sin(A) = a2 sin(B) = pq/2

Height: h

  • 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

Perimeter: P

P = 4a

Rhombus Calculations:

The following formulas, based on those above, are used within this calculator for the selected calculation choices.

  • Calculate B, C, D | Given A
    Given angle A calculate angles B, C and D
    • B = 180° - A
    • C = A
    • D = B
  • Calculate A, C, D | Given B
    Given angle B calculate angles A, C and D
    • A = 180° - B
    • C = A
    • D = B
  • Calculate a | Given P
    Given the perimeter calculate side a
    • a = P / 4
  • Calculate P | Given a
    Given side length a calculate the perimeter
    • P = 4a
  • Calculate B, p, q, h, P, K | Given a, A
    Given side length and angle A calculate the diagonals, perimeter, height, area and angles B, C and D
    • p = √( 2a2 - 2a2 cos(A) )
    • q = √( 2a2+ 2a2 cos(A) )
    • P = 4a
    • h = a sin(A)
    • K = ah
    • B = 180° - A
    • C = A
    • D = B
  • Calculate A, B, q, h, P, K | Given a, p
    Given side length and diagonal p calculate diagonal q, perimeter, height, area and angles A, B, C and D
    • A = arccos( 1 - (p2 / 2a2) )
    • q = √( 2a2 + 2a2 cos(A) )
    • h = a sin(A)
    • P = 4a
    • K = a2 sin(A)
    • B = 180° - A
    • C = A
    • D = B
  • Calculate A, B, p, h, P, K | Given a, q
    Given side length and diagonal q calculate diagonal p, perimeter, height, area and angles A, B, C and D
    • A = arccos( 1 + (q2 / 2a2) )
    • p = √( 2a2 - 2a2 cos(A) )
    • h = a sin(A)
    • P = 4a
    • K = a2 sin(A)
    • B = 180° - A
    • C = A
    • D = B
  • Calculate A, B, p, q, P, K | Given a, h
    Given side length and height calculate the diagonals, perimeter, area and angles A, B, C and D
    • A = arcsin(h/a)
    • p = √( 2a2 - 2a2 cos(A) )
    • q = √( 2a2 + 2a2 cos(A) )
    • P = 4a
    • K = a2 sin(A)
    • B = 180° - A
    • C = A
    • D = B
  • Calculate A, B, p, q, h, P | Given a, K
    Given side length and area calculate the diagonals, perimeter, height and angles A, B, C and D
    • A = arcsin(K/a2)
    • p = √( 2a2 - 2a2 cos(A) )
    • q = √( 2a2 + 2a2 cos(A) )
    • h = a sin(A)
    • P = 4a
    • B = 180° - A
    • C = A
    • D = B
  • Calculate a, A, B, p, q, P | Given K, h
    Given area and height calculate side length, diagonals, perimeter and angles A, B, C and D
    • a = K / h
    • P = 4a
    • A = arcsin(K/a2)
    • p = √( 2a2 - 2a2 cos(A) )
    • q = √( 2a2 + 2a2 cos(A) )
    • B = 180° - A
    • C = A
    • D = B
  • Calculate a, A, B, q, h, P | Given K, p
    Given diagonal p and area calculate the perimeter, height, side length, diagonal q and angles A, B, C and D
    • q = 2K / p
    • a = √(p2 + q2) / 2
    • P = 4a
    • A = arccos( 1 - (p2 / 2a2) )
    • h = a sin(A)
    • B = 180° - A
    • C = A
    • D = B
  • Calculate a, A, B, p, h, P | Given K, q
    Given diagonal q and area calculate the perimeter, height, side length, diagonal p and angles A, B, C and D
    • p = 2K / q
    • a = √(p2 + q2) / 2
    • P = 4a
    • A = arccos( 1 + (q2 / 2a2) )
    • h = a sin(A)
    • B = 180° - A
    • C = A
    • D = B
  • Calculate a, B, p, q, P, K | Given A, h
    Given angle A and height calculate side a, angles B, C and D, diagonals, perimeter and area
    • a = h / sin(A)
    • P = 4a
    • p = √( 2a2 - 2a2 cos(A) )
    • q = √( 2a2 + 2a2 cos(A) )
    • K = a2 sin(A)
    • B = 180° - A
    • C = A
    • D = B

References

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/)

Weisstein, Eric W. "Rhombus." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Rhombus.html

 

Cite this content, page or calculator as:

Furey, Edward "Rhombus Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.