This **rhombus calculator** can help you find the side, area, perimeter, diagonals, height and any unknown angles of a rhombus if you know 2 dimensions.

## What is a rhombus?

A rhombus refers to a quadrilateral having two simultaneous characteristics: sides are all equal *AND* the opposite sides are parallel. Please note that a rhombus having four right angles is actually a square.

## How does this rhombus calculator work?

Depending on the figures you know this *rhombus calculator* can perform the following calculations:

■ If Angle (A) is given then the other 3 angles will be computed:

B = 180° - A

C = A

D = B

■ The same goes in case Angle (B) is given:

A = 180° - B

C = A

D = B

■ If side (a) is available then the perimeter (P) will be calculated:

P = 4a

■ On the other hand if the perimeter (P) is given the side (a) can be obtained from it by this formula:

a = P / 4

■ When side (a) and angle (A) are provided the figures that can be computed are: perimeter (P), two diagonals (p and q), height (h), area (S_{A}) and the other three angles (B, C and D):

P = 4a

S_{A} = ah

h = a*sin(A)

p = √(2a^{2} - 2a^{2}*cos(A))

q = √(2a^{2}+ 2a^{2}*cos(A))

B = 180° - A

C = A

D = B

■ If side (a) and diagonal (p) are known then the other dimensions that can be estimated are the perimeter (P), height (h), diagonal (q), area (S_{A}) and all angles (A, B, C and D):

P = 4a

S_{A} = a^{2*}sin(A)

q = √(2a^{2} + 2a^{2}*cos(A))

h = a*sin(A)

A = arccos(1 - (p^{2} / 2a^{2}))

B = 180° - A

C = A

D = B

■ In case side (a) and diagonal (q) are the variables known then the perimeter (P), height (h), diagonal (p), area (S_{A}) and all the four angles (A, B, C and D) can be found:

P = 4a

S_{A} = a^{2}*sin(A)

p = √(2a^{2} - 2a^{2}*cos(A))

h = a*sin(A)

A = arccos(1 + (q^{2} / 2a^{2}))

B = 180° - A

C = A

D = B

■ When side (a) and height (h) are given the perimeter (P), diagonals (p and q), area (S_{A}) and the angles can be calculated:

P = 4a

S_{A} = a^{2}*sin(A)

p = √(2a^{2} - 2a^{2}*cos(A))

q = √(2a^{2} + 2a^{2}*cos(A))

A = arcsin(h/a)

B = 180° - A

C = A

D = B

■ If side (a) and area (S_{A}) are known the perimeter (P), diagonals (p and q), height and all the angles A, B, C and D can be determined:

P = 4a

p = √(2a^{2} - 2a^{2}*cos(A))

q = √(2a^{2} + 2a^{2}*cos(A))

h = a*sin(A)

A = arcsin(S_{A}/a^{2})

B = 180° - A

C = A

D = B

■ In case area (S_{A}) and height (h) are the variables known the perimeter (P), side length (a), diagonals (p and q) and all the angles (A, B, C and D) can be computed:

a = S_{A} / h

P = 4a

p = √(2a^{2} - 2a^{2}*cos(A))

q = √(2a^{2} + 2a^{2}*cos(A))

A = arcsin(S_{A}/a^{2})

B = 180° - A

C = A

D = B

■ When area (S_{A}) and diagonal (p) are provided the perimeter (P), side length (a), height (h), diagonal (q) and all the angles (A, B, C and D) can be calculated:

a = √(p^{2} + q^{2}) / 2

P = 4a

q = 2S_{A} / p

h = a*sin(A)

A = arccos(1 - (p^{2} / 2a^{2}))

B = 180° - A

C = A

D = B

■ If area (S_{A}) and diagonal (q) are given the side length (a), height (h), perimeter (P), diagonal (p) and the angles (from A to D) can be estimated:

a = √(p^{2} + q^{2}) / 2

P = 4a

p = 2S_{A} / q

h = a*sin(A)

A = arccos(1 + (q^{2} / 2a^{2}))

B = 180° - A

C = A

D = B

■ Finally, if the angle (A) and the height (h) are provided then the side length (a), perimeter (P), diagonal (p and q), area (S_{A}) and all the other three angles (B, C and D) can be obtained:

a = h / sin(A)

P = 4a

p = √(2a^{2} - 2a^{2}*cos(A))

q = √(2a^{2} + 2a^{2}*cos(A))

S_{A} = a^{2}*sin(A)

B = 180° - A

C = A

D = B

11 Aug, 2015