Slope and gradient conversion: degrees, percent, mm/m and ratios.

The five ways of saying it.

Every one of these describes the same thing — how much a surface rises or falls over a given horizontal distance — and every trade picked a different one.

• Degrees. The angle between the surface and horizontal. Roofers, joiners and anyone working from a protractor. Ranges 0° (flat) to 90° (vertical).
• Percent slope. Rise divided by run, times 100. Roads, ramps, accessibility standards, and most groundwork. A 100% slope is 45°, not vertical — this is the one that surprises people.
• Millimetres per metre (mm/m). The fall in millimetres over one metre of run. Plumbing, drainage and tiling, because it is directly measurable with a tape.
• Inches per foot. The same idea in imperial. Common in North American plumbing, usually as fractions: ¼ inch per foot, ⅛ inch per foot.
• Ratio, written 1:N. One unit of fall for every N units of run. Drainage and highway work. A bigger N is a shallower slope, which is the opposite of how every other unit behaves and a reliable source of confusion.

The underlying relationship is just the tangent of the angle. Percent is tan × 100, mm/m is tan × 1000, inches per foot is tan × 12, and the ratio 1:N has N equal to 1 ÷ tan.

Degrees to percent, mm/m and ratio.

Read across from whatever your level is showing. LevelerPro can display any of the first four directly, so you rarely have to convert by hand — but a spec written as 1:80 needs the last column.

Note how the columns stop being proportional as the angle grows. Below about 5° the relationships are near enough linear that you can scale them in your head; by 45° the tangent has run away and 45° is 100%, not 50%.

Ratios and percentages back to degrees.

Specifications are usually written as ratios, and levels usually read in degrees. This is the table for that direction.

A useful sanity check on any ratio: 1:N in mm per metre is simply 1000 ÷ N. So 1:80 is 12.5 mm/m, 1:40 is 25 mm/m, and 1:100 is 10 mm/m. No trigonometry needed, and at these shallow angles the error from ignoring the tangent is far below anything you could measure.

Doing it in your head.

For the shallow angles that cover most building work — say under 5° — two constants get you close enough to check a reading on site.

• Degrees to mm/m: multiply by 17.5. So 1° is about 17.5 mm/m, 0.5° is about 8.7 mm/m, 2° is about 35 mm/m. The exact factor at 1° is 17.46, so this is good to a fraction of a percent.
• Degrees to percent: multiply by 1.75. Same constant, shifted. 1° is 1.75%, 2° is 3.5%, 4° is 7%.
• Percent to mm/m: multiply by 10. This one is exact by definition, at any angle. 1% is 10 mm/m, 2.5% is 25 mm/m.

Going the other way, divide. A reading of 12.5 mm/m is 12.5 ÷ 17.5 ≈ 0.71°. All three break down as the angle grows, so above about 10° use the table.

Falls specified for common jobs.

These are the figures that come up repeatedly. They are here as a reference for reading your own measurements, not as a specification: drainage and accessibility are governed by building regulations that vary by country and by the particulars of the job, and the controlling document always wins.

Two of these deserve a note. Drainage has a maximum gradient as well as a minimum: run a foul pipe too steeply and the water outruns the solids, leaving them behind to block it. And gutter falls are far shallower than people assume — 1:600 is under 2 mm per metre, which is well below what a phone can resolve over a single reading. Set a gutter with a string line, not a level.

Three ways people get this wrong.

Reading percent as degrees

A 10% slope is 5.7°, not 10°. The two run close together at very small angles — 1% is 0.57° — and diverge steadily after that. A road sign warning of a 12% descent is describing about 6.8°.

Inverting the ratio

1:40 is steeper than 1:80. Because the run is the number that changes, a larger figure means the fall is spread over more distance. Anyone converting a spec of "minimum 1:80" into "anything up to 1:100 will do" has made the pipe shallower than allowed.

Confusing fall with pitch on a roof

Roof pitch is sometimes given in degrees, sometimes as rise:run, and the two halves of that ratio get swapped by different trades. A "4:12" roof in North American usage means 4 units of rise for 12 of run, which is 18.4°. Written as a drainage-style ratio the same roof is 1:3. Always establish which number is the rise before converting.

When in doubt, measure the thing rather than argue about the notation. Rest the phone on the surface, switch the leveler to mm/m, and compare that directly against 1000 ÷ N for whatever ratio the drawing specifies.