Geometry & trigonometry formulas
Sixteen connected concepts, each with a direct answer, a calculator, worked examples, and guided paths through the tools.
Start with geometry
Build from lengths to shapes.
Make sense of trigonometry
Connect a turning point to a wave.
Explore the coordinate plane
Describe position, distance, and movement.
Formula cheat sheet
The key formula from every guide. Select a topic for variables, a calculator, and step-by-step examples.
| Topic | Key formula |
|---|---|
| The Pythagorean theorem | a² + b² = c² |
| Law of cosines (cosine rule) | c² = a² + b² − 2ab cos C |
| Law of sines (sine rule) | a / sin A = b / sin B = c / sin C |
| Heron’s formula | Area = √[s(s − a)(s − b)(s − c)] |
| Radians & degrees | radians = degrees × π / 180 |
| Sine, cosine & tangent | sin θ = opposite / hypotenuse |
| Area & perimeter formulas | Rectangle: A = wh · P = 2(w + h) |
| Volume & surface area formulas | Cylinder: V = πr²h · S = 2πr(r + h) |
| Polygon angles & diagonals | Interior-angle sum = (n − 2) × 180° |
| Distance & midpoint formulas | d = √[(x₂ − x₁)² + (y₂ − y₁)²] |
| Slope & line equations | m = (y₂ − y₁) / (x₂ − x₁) |
| Arc length & sector area | s = rθ · A = ½r²θ |
| Transforming sine & cosine graphs | y = A sin(B(x − h)) + k |
| Translations, reflections & rotations | Translate: (x, y) → (x + a, y + b) |
| Similarity & scale factors | Length × k · Area × k² · Volume × k³ |
| Triangle medians & the centroid | G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3) |
Every concept, in one place
The Pythagorean theorem
The relationship that holds every right triangle together.
Law of cosines (cosine rule)
Pythagoras, extended to every triangle.
Law of sines (sine rule)
A shared ratio between sides and their opposite angles.
Heron’s formula
Find a triangle’s area using only its three sides.
Radians & degrees
Two ways to describe the very same turn.
Sine, cosine & tangent
Three ratios. One right triangle.
Area & perimeter formulas
The space inside is different from the distance around.
Volume & surface area formulas
What fits inside, and what covers the outside.
Polygon angles & diagonals
A triangle-based explanation for many-sided shapes.
Distance & midpoint formulas
Pythagoras meets the coordinate plane.
Slope & line equations
Describe a direction, then locate the line.
Arc length & sector area
Measure a slice of a circle.
Transforming sine & cosine graphs
Four parameters shape an entire wave.
Translations, reflections & rotations
Move a shape while keeping track of every vertex.
Similarity & scale factors
Why doubling the size changes more than you might expect.
Triangle medians & the centroid
Find the balance point of a triangle.