Sizu Riatto
Every Angle · Chapter 3

Right Angles

a² + b² = c². It finds a rafter from the roof's rise and half-span, checks that a patio is square, and puts a ladder's foot in the right place.

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Opens on the book's house and plot. Change any number to your own and press Calculate.

The ladder at 4 : 1 (for every 4 up, 1 out)

Enter two short sides, then press Calculate.

The formula

  • The long side c = √(a² + b²)
  • The angle at the first side = tan⁻¹(b ÷ a): a roof's pitch when a is the half-span and b the rise
  • Square check: measure the diagonal; if it matches c, the corner is a right angle. 3-4-5 (and 6-8-10, 1.2 × 3-4-5 …) is the builder's version
  • Ladder at 4 : 1 (UK HSE form): the foot goes out the height ÷ 4; length used = √(height² + foot²); angle = tan⁻¹ 4 = 75.96°
  • The US OSHA form measures a quarter of the ladder's length out: cos θ = ¼, θ = 75.52°. Ask which side the 4 is
The book's worked example, Chapter 3. The rafter to the wall line: √(4² + 2.6²) = 4.77 m, a 33.0° pitch. The footprint's diagonal is 12.81 m, the plot's 33.54 m; the 4.8 × 3.6 m patio should measure 6.0 m corner to corner (3-4-5 × 1.2). The ladder resting at 3.3 m for a 2.7 m camera: the foot 0.825 m (2.71 ft) out, 3.40 m of ladder at 75.96°.
Check it. Measure both diagonals of a rectangle: if they match each other and the calculator, it is square. Never work off the top three rungs.

Honest limits. A ladder angle is a starting point, not a safety certificate: firm level ground, three points of contact, a second person, and nothing on the roof. Anything above a ladder's safe reach is a professional's job. The book's house was worked out on paper from published figures, not surveyed by us: measure your own, and walk your own plot at night. Prices are illustrative US prices from November 2026, shown without a currency sign; put in your own. Everything stays in your browser: no sign-up, nothing stored.

These calculators go with Every Angle (Make It Add Up, Book 2), where every number on this page is worked by hand.