Science & Data

Geometry

Area, perimeter/circumference, surface area and volume of common shapes, plus the slope of a line — all written as functions with comma-separated arguments.

circle area(5)
triangle area(3, 4, 5)
cube volume(3)
slope(0, 0, 2, 4)

Length units

A bare number returns a plain number. If the side lengths share a length unit, the result is dimensioned: an area comes back as unit^2, a volume as unit^3, and a perimeter/circumference as the length unit itself.

circle area(5 meter)
cube volume(3 meter)
circle circumference(5 meter)

2-D shapes — area and perimeter

Function	Formula	Example
`circle area(r)`	π·r²	`circle area(5)`
`circle circumference(r)`	2·π·r (alias `circle perimeter`)	`circle circumference(5 meter)`
`square area(side)`	side²	`square area(4)`
`square perimeter(side)`	4·side	`square perimeter(4 km)`
`rectangle area(w, h)`	width × height	`rectangle area(3 meter, 4 meter)`
`rectangle perimeter(w, h)`	2·(w + h)	`rectangle perimeter(3 meter, 4 meter)`
`triangle area(base, height)`	½·base·height	`triangle area(6, 8)`
`triangle area(a, b, c)`	Heron's formula from three sides	`triangle area(3, 4, 5)`
`trapezoid area(a, b, height)`	½·(a + b)·height	`trapezoid area(4, 6, 3)`
`parallelogram area(base, height)`	base × height	`parallelogram area(5, 3)`
`ellipse area(a, b)`	π·a·b (semi-axes)	`ellipse area(3, 2)`

triangle area(6, 8)
triangle area(3, 4, 5)
trapezoid area(4, 6, 3)
ellipse area(3, 2)

3-D shapes — surface area and volume

Function	Formula	Example
`sphere volume(r)`	4/3·π·r³	`sphere volume(3)`
`sphere surface area(r)`	4·π·r² (alias `sphere area`)	`sphere surface area(3)`
`cube volume(side)`	side³	`cube volume(3)`
`cube surface area(side)`	6·side²	`cube surface area(3)`
`cylinder volume(r, h)`	π·r²·h	`cylinder volume(2 meter, 5 meter)`
`cylinder surface area(r, h)`	2·π·r·(r + h)	`cylinder surface area(2, 5)`
`cone volume(r, h)`	1/3·π·r²·h	`cone volume(2, 6)`
`cone surface area(r, h)`	π·r·(r + √(r² + h²))	`cone surface area(3, 4)`
`rectangular prism volume(l, w, h)`	l·w·h (alias `box volume`)	`box volume(2, 3, 4)`
`pyramid volume(l, w, h)`	1/3·l·w·h	`pyramid volume(3, 3, 9)`

sphere volume(3 feet)
cube volume(3 meter)
cylinder volume(2 meter, 5 meter)
cone volume(2, 6)
box volume(2, 3, 4)

Line slope

slope(x1, y1, x2, y2) returns (y2 − y1) / (x2 − x1).

slope(0, 0, 2, 4)
slope(2, 3, 6, 11)

Common mistakes

circle area(5 m) treats the radius as 5,000,000 — a bare m means million, not metre. Use a spelled-out length unit: circle area(5 meter).
area(5) or volume(2, 3, 4) error — there is no bare area or volume function. Name the shape: circle area(5), box volume(2, 3, 4).
Mixed length units such as rectangle area(3 meter, 4 feet) fall back to a plain number. Give both sides the same unit to keep the dimension.
A vertical line like slope(2, 1, 2, 5) has no finite slope and errors.

triangle area accepts either two arguments (base, height) or three (the side lengths, via Heron's formula).