Rise Over Run Calculator

The rise over run calculator starts with two measurements between chosen endpoints. Rise is the signed vertical change; run is the signed horizontal change. From those components it calculates slope, percent grade, a directed angle, and the diagonal distance between the endpoints. This measurement workflow is useful when the dimensions of a straight segment are known and you want to understand both its inclination and its direction.

Read measured displacement with the rise over run calculator

Choose a starting point before entering values. Moving upward gives positive rise and moving right gives positive run. Moving downward or left produces negative components. This page measures the directed angle counterclockwise from the positive horizontal axis, using atan2. The angle lies from −180° to 180°, with a leftward horizontal segment reported as 180°. Reversing the endpoints can change direction by a half turn while leaving the decimal slope unchanged.

Measure horizontal and vertical changes first

Record the height difference between endpoints rather than either endpoint's absolute height. If a line goes from height 2 to height 5, its rise is 3 in the selected unit.
Measure the horizontal separation, preserving its sign under your coordinate convention. The sloping edge is the diagonal, not the run. A tape placed along an incline therefore measures a different quantity.
Convert both components to the same unit before entering them. For example, a rise of 30 centimeters and run of 2 meters must become 0.3 and 2 meters, or 30 and 200 centimeters.
Read the directed angle together with the component summary and ratio. The diagonal output has the same unit as the inputs. All dimensionless outputs describe the relationship of those two measurements, and cannot identify their physical unit automatically.

Formulas and normalization of the measurements

Slope m = rise / run and grade = 100 × rise / run require nonzero run. The directed angle is θ = atan2(rise, run), and its degree value is θ × 180 / π. This retains quadrant information that atan(rise/run) alone would discard.
Diagonal length = √(rise² + run²). The implementation uses Math.hypot to avoid unnecessary intermediate overflow from squaring large inputs and underflow from squaring small ones. Length is always nonnegative even when one or both components are negative.
The normalized rise:run pair divides both components by the larger absolute component. Thus −3:4 becomes −0.75:1, and 3:−4 becomes 0.75:−1. These signs retain the direction, unlike an unsigned ratio of lengths.
The separate 1:n output divides by rise when both components are nonzero and the quotient is representable. It describes the algebraic slope: a negative n signals a negative quotient. For zero rise this form is unavailable; the normalized pair still describes a horizontal displacement.

Worked measurement examples

Rise 3 and run 4 give slope 0.75, grade 75%, directed angle ≈ 36.869898°, and diagonal length 5. The components form the familiar 3–4–5 right triangle, which provides an independent check of the distance calculation.
Rise −0.6 and run 2.4 describe a descending segment. Slope is −0.25, grade is −25%, angle ≈ −14.036243°, and distance ≈ 2.473863 in the shared unit. Its normalized pair is −0.25:1, while the slope ratio reads 1:−4.
Rise 3 and run −4 point upward and left. The directed angle is ≈ 143.130102°, but the quotient is −0.75. A negative slope is therefore compatible with a positive directed angle in the second quadrant.
For a vertical displacement with rise 5 and run 0, the direction is 90° and distance is 5. Slope and grade are undefined. Setting both components to zero removes the direction entirely and produces a validation message instead of an arbitrary angle.

Measurement quality and display limits

The rise over run calculator uses the entered changes exactly as represented by browser numbers, then rounds ordinary displays to at most six decimal places. Extreme magnitudes use six significant digits. Approximate display values should not be reused as more precise measurements. A result that overflows or underflows the finite numeric range is marked unavailable; another representable result, such as direction, can remain useful. The diagram labels signed components but draws a schematic right triangle with dimension magnitudes, so it is not a coordinate plot or a scale drawing. Uncertainty in the original dimensions carries into the outputs. For roof terminology use the pitch page; for changing an existing slope or grade representation use the general conversion hub.

Frequently Asked Questions

Why does this page show 135° for rise 1 and run −1?

The displacement points into the upper-left quadrant. Its atan2 angle is 135° from the positive horizontal axis. The slope hub instead reports the principal inclination of −45° for the same quotient.

Can I enter feet for rise and inches for run?

Convert first. For instance, one foot of rise over twenty-four inches of run is 12/24 = 0.5, not 1/24. Matching units are essential for a meaningful dimensionless slope.

What unit does the calculated diagonal use?

It uses the common unit of rise and run. Enter both in meters to obtain meters, or both in inches to obtain inches. The neutral interface deliberately does not infer a unit.