Slope vs Grade vs Pitch: The Same Number in Three Trades

Three trades, three words, one number. A math teacher says the line has a slope of 0.5. A site engineer says the drive has a 50% grade. A roofer says it is a 6:12 pitch. All three are describing the identical surface, and the only thing separating them is what each trade divides by and what it multiplies the answer by afterwards.

Confusing them is expensive. Reading a 100% grade as a 90 degree wall, or cutting rafters off the full span instead of half, are mistakes that show up as scrapped material rather than as a red mark on homework.

The short answer

Every one of them starts with the same division. Slope is the raw result, grade scales it by 100, pitch scales it by 12, and the angle is the only one that is not a simple multiple of the others.

Slope: the math version

Slope is the plain quotient, written m, and it is the form everything else is built from. Two points, subtract, divide:

Slope keeps its sign, which the trade versions usually drop. A slope of −0.5 falls half a unit per unit right; a roofer would still call that a 6:12 pitch and let the drawing say which way it falls. Slope is also the only one of the four that is happy to be undefined — a vertical line has no slope at all, which is not the same as a slope of zero.

If you want the full treatment, start with what slope is, then run your numbers through the slope calculator.

Grade: the civil version

Grade is slope as a percent. Multiply by 100 and add a sign convention: positive climbs in the direction of travel, negative falls. Highway signs, site plans, drainage drawings and earthworks all speak in grade.

The reason civil work prefers percent is that the numbers land in a comfortable range. A road at 0.06 slope reads awkwardly; a 6% grade is instantly meaningful, and 6% is about the practical maximum for a sustained interstate climb. Drainage works at the other end of the scale — a parking lot might fall at 1.5%, and a 1/4 inch per foot drain line is 2.08%.

Grade is also where the unit trap lives. "A quarter inch per foot" is already a ratio with mismatched units — inches over feet. Convert one side before dividing, or you are out by a factor of 12. The percent grade calculator handles the conversion, and the pipe slope calculator applies the code minimums by diameter.

Pitch: the roofing version

Pitch is slope scaled to a 12 inch run and written as a ratio, x:12. The 12 never changes, so a roofer only ever quotes the first number. A 6:12 roof rises 6 inches per foot of horizontal run.

The 12 is not arbitrary — it is what makes the measurement possible with a two foot level and a tape, standing at a gable end. Mark 12 inches along a level held horizontal, measure down to the roof, read the rise. No trigonometry, no calculator, no climbing on the roof.

Two things about pitch trip people up. First, the run is measured to the centre of the ridge, which is half the building span, not the full width. Second, the pitch triangle is not the rafter — you need the rafter multiplier, √(rise² + run²) ÷ run, to turn horizontal run into material length. The roof pitch calculator returns both.

Converting between them

Where degrees fit in

Degrees are the odd one out. Slope, grade and pitch are all linear rescalings of the same quotient, so converting between them is a single multiplication. Degrees come from a tangent, which is not linear — doubling the slope does not double the angle.

That is why the table above has even steps in the first three columns and uneven ones in the last. From 0.5 to 1.0 slope, grade goes 50% to 100% and pitch goes 6:12 to 12:12, but the angle moves only 26.57° to 45°. The steeper things get, the more slowly the angle changes — an infinite slope is still only 90°.

Use degrees when you are setting something that is measured in degrees: a miter saw, a solar array tilt, an excavator's grade indicator. Do not use them for material takeoffs, because the multiplier you need there is the ratio, not the angle.

Which one to use on site

• Framing a roof — pitch. Everyone on the crew already speaks it, and the rafter multiplier falls straight out of it.
• Running a drain or a sewer — inches per foot, which is a pitch in disguise. Code tables are written that way, so stay in those units and let the calculator convert.
• Site work, driveways, parking, roads — percent grade. It is what the drawings, the grade stakes and the equipment all use.
• Accessibility ramps — ratio (1:12) for the code check, percent for the drawing. Both appear in the ADA standards.
• Solar panels, saw settings, anything with a protractor — degrees.
• Algebra homework — slope, as a fraction. Teachers want the exact fraction, not a rounded decimal.

The rule of thumb: use whatever unit the next person downstream is going to read. Convert once, at the boundary, and write down which unit you handed over — most of the mistakes below start with a number that lost its label.

Mistakes that cost money

• Reading percent grade as a share of vertical. 100% is 45°, not 90°. There is no ceiling on percent grade.
• Mixing inches and feet. A rise in inches over a run in feet is out by 12. This is the single most common error in drainage work.
• Using the full span for a roof run. The run is wall to ridge centre. Using the full width doubles every rafter you cut.
• Treating the pitch triangle as the rafter length. The rafter is the hypotenuse — apply the multiplier.
• Quoting a pitch without the second number. "A six pitch" is only unambiguous among roofers. On a drawing, write 6:12.
• Rounding too early. Convert once at the end. Rounding a slope to two decimals and then multiplying by a 40 ft run puts you inches out.

Every one of these is a labelling problem, not an arithmetic problem. Write the unit next to the number, every time, and most of this class of mistake disappears on its own.