Field guide
Keep rise, run and slope expressions consistent
A useful result starts with the right distance and a clear direction.
Choose the question before entering numbers
This percent slope calculator helps you check the relationship between a signed elevation change and a horizontal distance. You can calculate slope from rise and run, find the rise from a known horizontal run and slope, or find the run from a known rise and slope. A fourth mode converts a slope expression without inventing a length. Select the known quantities first: the page only uses the visible inputs, and hidden values do not become extra constraints.
Use the calculation for a straight segment with a defined start and end. It can help review a grade note, compare equivalent expressions in a drawing, or check a simple height difference. It does not model intermediate terrain, locate grade breaks, or decide whether the segment meets a construction specification. Record the source and purpose of your inputs when the result will accompany a technical handoff.
Use horizontal run and a common length unit
Run is the horizontal projection of the segment. It is not the distance measured by a tape lying along the slope, nor the length of a winding route across changing terrain. Rise is the end elevation minus the start elevation. If your source only supplies an inclined distance, first reduce it using independently known geometric information; substituting it directly for run changes the denominator and therefore the calculated grade.
Both lengths must use the same unit before calculation. A rise written in millimetres and a run written in metres cannot be divided as if their numeric values were already comparable. The unit selector records a common label; it does not convert either input. For example, convert 250 millimetres to 0.25 metres before combining it with a 5 metre horizontal run. The resulting ratio is dimensionless, while the reported rise, run and straight slope length retain the chosen unit.
A complete example: one unit of rise in twenty
Enter rise 1 and horizontal run 20. The gradient is 1 divided by 20, or 0.05; multiplying by 100 gives 5%. The angle from horizontal is approximately 2.862405 degrees, and the horizontal-to-vertical ratio is 20 H : 1 V. The straight inclined length is approximately 20.024984 in the same length unit. This example is synthetic and describes the arithmetic, not an observed site or a recommended design.
Reverse the travel direction and use rise −1 with the same positive horizontal run 20. The percent and angle become negative, showing downhill movement from the chosen start to end. The H:V magnitude remains 20:1, and the length remains positive. A negative run is not used to describe downhill travel here. Keeping direction in the signed rise prevents two negative inputs from accidentally turning a descending segment into a positive grade.
Percent slope and angle answer different questions
A percentage describes vertical change per hundred units of horizontal run. An angle describes inclination from horizontal. They are connected through the tangent relationship rather than a fixed multiplication between percent and degrees. This is why 5% is not 5°, and why 100% corresponds to 45° rather than a vertical line. As the line approaches vertical, a finite rise is divided by a progressively smaller horizontal run.
For a source example published by the USGS, a rise of 1,000 feet over a horizontal run of 2,000 feet gives a 50% slope. The inverse tangent of 0.5 is approximately 26.565051°. Those values provide a convenient independent check of the input convention. Do not take a rounded display value, copy it into several later calculations, and expect to retain the precision of the original inputs. The downloadable report keeps the calculated numeric values.
Read the ratio order rather than guessing it
This page always labels a slope ratio as horizontal to vertical: n H : 1 V for a nonlevel segment. A ratio of 20 H : 1 V therefore means twenty horizontal units per one vertical unit. Some plans and textbooks instead write vertical to horizontal, such as 1 V : 20 H. The same geometry can use either notation, but an unlabelled 1:20 or 20:1 is not enough to establish which convention the author intended.
The ratio input accepts a nonnegative horizontal number n and a separate uphill or downhill choice. Enter 20 and choose downhill to represent a −5% grade. A level line cannot be represented by a finite n with a vertical denominator of one, so use zero percent or zero degrees; the output then states 1 H : 0 V. A vertical direction is 0 H : 1 V, with its up or down sign shown separately.
Solve a missing length only when the conditions are sufficient
With a positive known horizontal run and a finite grade, the rise equals run multiplied by the gradient. For run 40 and grade −2.5%, the gradient is −0.025 and the rise is −1. With a known rise of −1 and the same grade, the corresponding run is 40. In either case, the sign describes the chosen start-to-end direction. A positive rise paired with a negative slope is inconsistent and is rejected instead of producing a negative horizontal distance.
Slope alone determines percent, angle and ratio but no absolute rise or distance. A 5% line could rise 1 over 20 or 10 over 200. Similarly, zero rise and zero slope do not determine how long a level segment is. The calculator reports insufficient or contradictory conditions explicitly. It does not fill an unknown distance with zero simply to populate the result table.
Distinguish a vertical segment from a zero-length segment
When horizontal run is zero and rise is nonzero, the segment is vertical. Its angle is +90° or −90°, its H:V ratio is 0:1, and its percent slope has no finite value. The result records that special case without exporting a fabricated numeric percentage. You can also supply a known nonzero rise and a matching vertical angle to calculate zero horizontal run. A positive horizontal run paired with a vertical angle is contradictory.
When both rise and run are zero, there is no directed segment from which to define a slope. The expression 0 divided by 0 is undefined; it is not a valid zero-percent grade. A genuinely level segment instead has zero rise and a positive horizontal run. This distinction is useful when checking repeated endpoints, empty distance records or a data entry mistake that would otherwise look like a harmless flat result.
Review the report before passing it onward
The result table presents rise, horizontal run, straight slope length, percentage, angle and ratio together. The small diagram helps explain the direction and geometric relationship; it does not show ground obstacles, surface roughness or an approved profile. The straight length is calculated from the right-triangle relationship and is not a route chainage through multiple changes of grade. Review each quantity against the task that originally prompted the calculation.
Download a CSV for tabular review or a JSON report that keeps the active known inputs, selected mode, unit, result status, calculation relationship, version and time. The CSV protects textual input and note fields against spreadsheet formula interpretation. Changing a value invalidates the old result so it cannot be mistaken for a current calculation. Restore last inputs returns the previous successful input set for a new calculation; Clear removes the in-page session.
Precision and appropriate use
Display values use up to six decimal places, with scientific notation for very small nonzero results. Calculated outputs use finite browser numeric precision, while the original input strings remain in the JSON record. Decimal angles accept at most twelve fractional places. Very large or very small combinations that cannot be represented reliably are rejected rather than shown as infinity, a false zero or a misleading right angle.
The calculator does not automatically approve a road, drainage design, excavation slope or accessible route. Such decisions depend on the applicable requirements and project conditions, not just a converted percentage. Keep any design check separate from this arithmetic record. For a final independent check, divide the reported rise by run where defined, compare the resulting gradient with the percentage divided by one hundred, and confirm that the chosen travel direction agrees with the sign.