A rhombus is a four-sided shape where every side is the same length — think of a "squashed square." This calculator finds its area, perimeter, and diagonals from whichever pair of measurements you already have, whether that's the diagonals, a side with its height, or a side with an angle.

How the Rhombus Calculator works

All three area formulas describe the same shape from different angles: A = ½·d₁·d₂ uses the diagonals directly, A = base·height treats the rhombus like a slanted parallelogram, and A = s²·sinθ uses the side length and an interior angle. Because a rhombus's diagonals always bisect each other at a right angle, knowing any two of {side, height, angle, d₁, d₂} is enough to derive all the others — that's why this calculator can compute the full set of measurements no matter which input mode you pick.

Inputs and what they mean

In Side + Height mode, the height can never be larger than the side — if it were, the shape wouldn't close up into a rhombus. In Diagonals mode, both diagonals must be positive; the calculator derives the side automatically using the Pythagorean relationship between the half-diagonals. In Side + Angle mode, the angle is any one of the four interior angles, entered in degrees between 0° and 180° — since opposite angles are equal, it doesn't matter which one you measure.

Limits and edge cases

When the interior angle is exactly 90°, the rhombus becomes a square and both diagonals come out equal — try the Side + Height example with height equal to the side to see this. This calculator assumes a simple (non-self-intersecting) rhombus with positive side lengths; entering a height greater than the side, or an angle of 0° or 180°, describes a degenerate shape with no area, so those inputs are rejected.

Use finite values with magnitude at most 1e50. Expressions support pi, sqrt(), fractions and arithmetic. Angles are limited to 1e12 degrees. Units are mathematical; geometry alone does not establish physical safety. Read the linked values, named formulas, diagram coordinate table and any branch or parameter comparison.