Roof pitch calculator

Enter rise and run in any consistent length unit; the tool returns slope ratio and percent, pitch_in_12, angle from arctangent of rise over run, hypotenuse of the right triangle, and the classic rafter multiplier so you can scale any run into board length. When run is zero the geometry is undefined, so the API returns a clear invalid_input error instead of dividing by zero.

How to call the API and what comes back

Rise must be greater than or equal to zero and at most one trillion; run must be strictly positive, at least one times ten to the minus fifteen, and at most one trillion, using the same length unit as rise. Send a JSON body with two required finite numbers: rise (aliases R, height, vertical, rise_in) and run (aliases H, horizontal, span, run_in). On success the response echoes rounded rise and run, sets pitch_ratio to a simplified integer ratio when both inputs are whole numbers otherwise a compact rise colon run string, pitch_label to the familiar X-slash-twelve form, pitch_in_12 to twelve times rise over run, slope_ratio and slope_percent to the unit slope and percent grade, angle_degrees and angle_radians to the arctangent results, rafter_multiplier and hypotenuse to the hypot-based length factor and absolute hypotenuse, formula to a short English formula line, message to a one-line summary, and steps to an ordered array of substitution lines you can show in UI or assert in tests. Failed validation—missing fields, non-finite numbers, negative rise, zero or negative run, or values outside absolute limits—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

Measure rise and run with the same tape and unit; mixing inches of rise with feet of run silently doubles or multiplies the pitch and ruins the multiplier. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Prefer this capability when you already have rise and run and need ratio, angle, and factor; if you only know degrees, invert with tangent to recover rise for a chosen run first. For a common gable, run is often half the building width minus wall thickness adjustments—confirm whether your span is full width or half-span before calling the API. Classic teaching pairs: six and twelve yield a six-twelve pitch near twenty-six point five seven degrees and multiplier about one point one one eight; four and twelve is a gentler four-twelve; twelve and twelve is a steep forty-five degree plane with multiplier root two; rise zero and run twelve demonstrates the flat-roof limit; run zero demonstrates the hard invalid_input path. This landing targets people searching for a roof pitch calculator, rise over run, slope angle in degrees, or rafter length multiplier; it is not a full lumber estimator, not a truss designer, and not a building-code checker for minimum pitch by climate or covering. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when integrators deliberately send a zero run. Round-trip checks are easy: recompute atan of rise over run in degrees and hypot over run by hand and confirm they equal the published angle_degrees and rafter_multiplier within the same twelve-decimal rounding.