RectangleVEXQOMIRA / GEOMETRY 07
Rectangle Vexqomira

Formulas, without the guesswork.

Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.

Length and width

A = ab; P = 2(a+b); d = √(a²+b²)

Inputs: Length a (length units); Width b (length units).

Apply this formula ↗

Diagonal and one side

b = √(d²−a²)

Inputs: Diagonal d (length units); Known side a (length units).

Apply this formula ↗

Area and one side

b = A/a

Inputs: Area A (square units); Known side a (length units).

Apply this formula ↗

Perimeter and one side

b = P/2−a

Inputs: Perimeter P (length units); Known side a (length units).

Apply this formula ↗

Reading the notation

√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.

Do not use a sloping distance as a side. A diagonal must exceed the known adjacent side.

Reference reading: Rectangle at Wolfram MathWorld.