Three notations, one line
A slope is a rise divided by a run, and everything else is presentation. Percent grade is that ratio times a hundred. A ratio written 1 in 12 is the same fraction with the numerator forced to one. Degrees is the arctangent of it. The conversions are:
percent = 100 x rise / run, ratio X = run / rise, degrees = arctan(rise / run)
The trap is that the first two are linear in the ratio and the third is not. A 100 percent grade is 45 degrees, not 90. A 50 percent grade is 26.565 degrees, not 22.5. Halving a percentage does not halve the angle, and the discrepancy is small at shallow slopes and enormous at steep ones. At the flat end you can get away with treating them as proportional: 2 percent is 1.146 degrees and 4 percent is 2.291, close enough to double for most purposes. By 30 percent that approximation is already off by a degree and a half.
| Ratio | Percent | Degrees | Per foot | Per metre | Typical use |
|---|---|---|---|---|---|
| 1 in 100 | 1.000% | 0.573° | 1/8 in | 10 mm | Long shallow surface drainage |
| 1 in 96 | 1.042% | 0.597° | 1/8 in | 10.4 mm | The 1/8 in per foot figure exactly |
| 1 in 50 | 2.000% | 1.146° | 1/4 in | 20 mm | Grading away from a foundation |
| 1 in 48 | 2.083% | 1.194° | 1/4 in | 20.8 mm | The 1/4 in per foot figure exactly |
| 1 in 20 | 5.000% | 2.862° | 0.60 in | 50 mm | Below the threshold usually treated as a ramp |
| 1 in 12 | 8.333% | 4.764° | 1 in | 83 mm | The commonly cited ramp design target |
| 1 in 8 | 12.500% | 7.125° | 1.5 in | 125 mm | Steep driveway, loading slope |
| 1 in 4 | 25.000% | 14.036° | 3 in | 250 mm | Very steep drive, roadway warning grade |
| 1 in 2 | 50.000% | 26.565° | 6 in | 500 mm | 6 in 12 roof pitch |
| 1 in 1 | 100.000% | 45.000° | 12 in | 1000 mm | 12 in 12 roof, angle of repose territory |
Drainage: where the shallow numbers come from
The figure that governs most site and paving work is a quarter inch of fall per foot of run, which is 2.083 percent, or 1 in 48. It is shallow enough to walk on without noticing and steep enough that water leaves rather than pooling, and it survives the tolerance of hand-laid work. An eighth of an inch per foot, 1.042 percent, turns up on long runs where a quarter inch would accumulate into too much drop over the distance, but it only works on surfaces smooth and accurately laid enough to hold that slope, because a quarter inch of settlement anywhere along the run cancels it.
Grading soil away from a building is usually specified as a percentage rather than a fall per foot, and 2 percent, or six inches over ten feet, is a figure that recurs. The point is to move surface water away from the foundation before it can find its way down beside it. Soil settles, so building the fall in at more than the target is the sensible direction to err. As with everything else on this page, what is actually required where you are is set locally.
Pipe falls are their own subject and this calculator only converts the number. Drainage pipe has both a minimum slope, below which solids do not carry, and a practical maximum on some systems where too much fall lets water outrun the solids. The right figure depends on the pipe diameter, the material and the code in force, and a fall per foot converted here is not a substitute for looking it up.
Ramps, and why 1 in 12 is a target and not a guarantee
The number everyone knows for an accessible ramp is 1 in 12: one unit of rise for every twelve of run, 8.333 percent, 4.764 degrees. It is the most widely used design target for ramps intended to be usable by someone in a wheelchair, and it is a reasonable starting point for any ramp you are designing by hand.
It is not, on its own, compliance. Accessibility requirements for ramps are regulated, and the applicable standard depends on where you are building and what kind of building it is, with different rules for public and commercial buildings than for private dwellings. The slope is one clause among many: the standards also cover the maximum rise permitted before a level landing is required, the size and placement of landings, ramp width, cross slope, surface and slip resistance, edge protection, and handrails on both sides. A run that hits 8.33 percent exactly and has no landing partway up, or no handrail, or a cross slope that tips a chair sideways, is not an accessible ramp.
So use this page to get the slope arithmetic exactly right, and use the standard that governs your project to find out what else the ramp needs. If the ramp serves a public or commercial building, or is being built under a permit, ask the authority reviewing it which standard applies before the design is fixed rather than after the concrete is poured.
Slope distance, and the thing people forget to buy
A surface laid on a slope is longer than the horizontal distance it covers, by a factor of the square root of one plus the slope squared. At the shallow end this rounds away to nothing: a 2 percent grade over 100 feet adds a quarter of an inch of surface length, which nobody is going to order material for. At 1 in 12 it is 0.35 percent, still small. At a 6 in 12 roof pitch the same factor is 1.118, which is a very real 12 percent more material than the plan view suggests, and it is the reason roofing and rafters are never estimated off a footprint.
The crossover is somewhere around 10 percent, below which you can quote the level distance and be inside your waste allowance, and above which you cannot. This page reports the slope distance alongside the rise for exactly that reason: it is a one-line check that costs nothing and occasionally saves a second delivery.
Questions people ask
What is a 1 in 12 slope as a percentage and in degrees?
A 1 in 12 slope is 8.333 percent and 4.764 degrees. The percent comes from dividing 1 by 12 and multiplying by 100; the angle is the arctangent of 1 divided by 12. In fall-per-foot terms it is exactly one inch of rise for every foot of run, which is the easiest way to lay it out with a level and a tape. It is worth noticing that 4.76 as a degree figure and 8.33 as a percent describe the same line, because those two numbers get swapped surprisingly often in conversation and in print.
How do I convert percent grade to degrees?
Take the arctangent of the percentage divided by 100. A 2 percent grade is arctan(0.02), which is 1.146 degrees. A 25 percent grade is arctan(0.25), which is 14.036 degrees. Going back the other way, multiply the tangent of the angle by 100. The relationship is not linear, which matters more than people expect: a 100 percent grade is 45 degrees, so anything you might assume about percentages scaling to degrees breaks down long before you get there. Below about 10 percent you can treat 1 percent as roughly 0.57 degrees and be close enough for site work.
What slope do I need for drainage?
A quarter inch of fall per foot, which is 2.083 percent or 1 in 48, is the figure most surface and paving work is built to. An eighth of an inch per foot, 1.042 percent, is used on long runs but only where the surface is smooth and laid accurately enough to hold the slope over the whole distance. For grading soil away from a building, 2 percent is a commonly used target and building in a little more is sensible because soil settles. Drainage pipe is a separate question with its own minimum and sometimes maximum falls that depend on diameter, material and the code in force where you are.
Is a 1 in 12 ramp legally compliant?
Not by itself. One in twelve is the most widely used design target for the slope of a ramp meant to be used by someone in a wheelchair, and it is the right number to design to in the absence of other information. But accessibility requirements are regulated and cover much more than the gradient: the maximum rise before a level landing is required, the size of those landings, the width, the cross slope, the surface, edge protection and handrails all form part of the standard, and the standard that applies depends on your jurisdiction and on whether the building is public, commercial or a private dwelling. Design to 1 in 12, then check the applicable standard for everything else, and ask the authority reviewing the work if a permit is involved.
How much longer is a sloped surface than its horizontal run?
Multiply the run by the square root of one plus the slope squared. At 2 percent that factor is 1.0002, which is a quarter of an inch over a hundred feet and safely ignorable. At 1 in 12 it is 1.0035. At a 6 in 12 roof pitch it is 1.118, so a roof covers 12 percent more area than its footprint, and at 12 in 12 it is 1.414. The practical rule is that below roughly 10 percent you can order material off the level dimension and let the waste allowance absorb the difference, and above that you cannot.
Why does my laser level disagree with the percentage I calculated?
Usually because of what the two are measuring over. A grade is rise over horizontal run, and a tape stretched along a sloping surface is measuring slope distance, not run. At shallow slopes the difference is invisible, but by 25 percent the slope distance is 3 percent longer than the run and your percentage comes out low. The other common cause is measuring to different reference points at each end, particularly on rough ground where the top of the soil and the top of the finished surface are not the same thing. Fix the reference first, then argue about the arithmetic.