How this instrument works
Slope is the ratio of vertical change to horizontal change, rise divided by run, and this sheet takes both numbers as direct physical measurements rather than derived values: the height of a ramp and the horizontal distance it covers, or a roof's vertical rise and its horizontal span. Divide one by the other and the result, slope = rise ⁄ run, describes the same steepness a carpenter, roofer, or ramp builder reads off a tape measure and a level, with no coordinate plane involved at all.
This is a different starting point than the site's Slope Calculator, which computes the identical ratio from two plotted (x, y) points, subtracting one pair of coordinates from the other to get its own rise and run before dividing. Here there is no plane and no pair of points — rise and run are simply read directly off the object itself, a construction detail rather than an algebra exercise. The division that follows is the same either way; only the source of the two numbers differs.
A rise of zero returns a slope of exactly zero regardless of how long the run is — a flat, level surface with no climb at all. Builders often express the same ratio as a rise-to-run notation like '1-in-12' for wheelchair ramps, or as a percentage for road grades, by multiplying the slope by 100; a slope of 0.75 and a ratio described as '3 in 4' are the identical steepness stated two different ways.
- Measure the vertical change directly and enter it into Rise (vertical change).
- Measure the horizontal change directly and enter it into Run (horizontal change).
- Read Slope (rise ⁄ run): the steepness ratio between the two measurements.
- Keep both measurements in the same unit — feet with feet, metres with metres — so the ratio comes out unitless and comparable.
Worked example — a ramp rising 3 ft over 4 ft
A wheelchair ramp climbs 3 feet of vertical rise over a horizontal run of 4 feet, both measured directly with a tape and a level rather than read off any coordinate plane. The slope is simply slope = 3 ⁄ 4 = 0.75, a steepness figure that describes the same incline whether it's read as a decimal, as the fraction 3⁄4, or as the ratio '3 in 4'.
Compare a shallower version of the same ramp built over a longer run: keep the rise at 3 feet but stretch the run to 12 feet, and the slope drops to 3 ⁄ 12 = 0.25, a gentler climb across the same height. Only the run changed, yet the resulting steepness ratio fell to a third of its original value — slope tracks the run in the denominator, so a longer run always eases the climb for a fixed rise.
Questions
What is rise over run?
The ratio of vertical change to horizontal change, slope = rise ⁄ run, taken here as two lengths measured directly off a physical object like a ramp or a roof rather than computed from coordinate points. A rise of 3 over a run of 4 gives a slope of 0.75, meaning the surface climbs three-quarters of a unit for every unit it runs horizontally.
How is this different from the site's Slope Calculator?
That page starts from two (x, y) coordinate points and subtracts one pair from the other to get its own rise and run before dividing. This page skips that step and takes rise and run as measurements already in hand, straight from a tape measure or a level — the more natural starting point for construction and physical-object contexts rather than coordinate geometry.
What does a rise of zero mean?
A perfectly flat, level surface. Dividing zero by any run still gives a slope of exactly zero, regardless of how long the horizontal run happens to be, since there is no vertical climb to measure in the first place.
How do I convert this slope into a percentage grade?
Multiply the slope by 100. A slope of 0.75 becomes a 75% grade, meaning 75 units of vertical rise for every 100 units of horizontal run — a notation common on road signs and construction drawings, and interchangeable with the plain ratio this sheet returns.
Can rise and run be entered in any unit?
Yes, as long as both use the same one. Feet paired with feet, or metres with metres, produce a unitless ratio; mixing feet for the rise with metres for the run would distort the resulting slope, since the ratio only means what it claims when both measurements share a unit.