Calculate pipe slope as a percent and inches per foot from fall and run, or find the fall or run for a slope such as 1/4 inch per foot or 1:40.
Pipe Slope References For Plumbing, Sewer, and Drainage
| Usage | Common Slope | Percent | Typical Use |
|---|---|---|---|
| Small fixture drain lines up to 2 in | 1/4 in per ft | 2.0833% | Lavatories, sinks, smaller branch drains |
| Example drain sizes 3 to 6 in | 1/8 in per ft | 1.0417% | Main horizontal drains and larger pipe runs |
| Building sewer line | 1/8 in per ft to 1/4 in per ft | 1.0417% to 2.0833% | Building sewer laterals and site sewer runs |
| Very flat large-diameter runs where allowed | 1/16 in per ft | 0.5208% | Special cases only where permitted |
- All Slope Calculators
- Grade Slope Calculator
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- Two Point Slope Calculator
- Compound Pipe Angle Calculator
Pipe Slope Formula
Pipe slope is the vertical fall of a pipe divided by its horizontal run. When you know the fall and the run, the slope as a percent is:
Slope (%) = (Fall / Run) * 100
The same ratio written as a decimal is the grade, and multiplying the grade by 12 gives the drop in inches for every foot of run:
Grade = Fall / Run
Slope (in/ft) = Grade * 12
Rearrange the first formula to find the fall needed for a target slope over a known run, or the run a given fall covers at a set slope:
Fall = (Slope / 100) * Run
Run = Fall / (Slope / 100)
When you work from surveyed elevations instead of a measured drop, the fall is the difference between the two invert elevations, and the slope follows from the run:
Fall = Upstream invert - Downstream invert
Variables:
- Slope is the steepness of the pipe, usually written as a percent but also as inches per foot, a decimal grade, or a 1:n ratio
- Fall (also called drop) is the vertical distance the pipe descends from its upstream end to its downstream end
- Run is the horizontal length the pipe covers, measured level rather than along the pipe
- Grade is the fall divided by the run as a plain decimal, the same value as slope before it is multiplied by 100
- Upstream and downstream inverts are the inside-bottom elevations at the stated ends of the run, measured from a common datum; downstream can be higher in an adverse slope
Pick what you want to solve for at the top of the calculator. The default slope mode takes the drop and the run and returns the slope as a percent, a grade, inches per foot, a ratio, and an angle. Switch to the drop mode when you know the slope and run and need the fall, or to the run mode when you know the slope and drop and need the length. The invert mode takes two flow line elevations and a run and returns the fall and the slope, and it flags an adverse slope when the downstream invert sits higher than the upstream one. Under Display and reference comparison, select decimal places and an optional exact fractional reference. A numerical match does not establish code applicability, exceptions, flow capacity or compliance. Positive fall is downhill; run mode rejects mismatched signs rather than turning a negative distance positive.
Minimum Drainage Pipe Slopes by Size
The first table reproduces the fractional size references found in NYC Plumbing Code Table 704.1. It is a reference example, not a determination of the code adopted for your project. Confirm the applicable edition, amendments and service exceptions; some applicable IPC provisions require 1/4 in/ft for piping upstream of a grease interceptor. The second table shows mathematical conversions.
| Pipe diameter | Minimum slope (inch per foot) | Minimum slope (percent) |
|---|---|---|
| 2.5 in or smaller | 1/4 in/ft | 2.08% |
| 3 in to 6 in | 1/8 in/ft | 1.04% |
| 8 in or larger | 1/16 in/ft | 0.52% |
Slope alone does not establish self-cleansing velocity. Flow, pipe size, roughness, depth, service and required uniformity also matter. The calculator compares unrounded values with exact fractional references rather than the rounded percentages displayed in the table.
| Slope (percent) | Inches per foot | Grade (ft/ft) | Fall-to-run ratio |
|---|---|---|---|
| 0.5% | 0.06 in/ft | 0.005 | 1:200 |
| 1.04% (1/8 in/ft) | 0.125 in/ft | 0.0104 | 1:96 |
| 2.08% (1/4 in/ft) | 0.25 in/ft | 0.0208 | 1:48 |
| 2% | 0.24 in/ft | 0.02 | 1:50 |
| 4% | 0.48 in/ft | 0.04 | 1:25 |
Example Problems
Example 1: Find the slope from a measured drop.
A 24-foot branch drain falls 6 inches from one end to the other. Put the fall and the run in the same units, then divide and multiply by 100. The run of 24 feet is 288 inches:
Slope = (6 / 288) * 100 = 2.08 percent, which is 1/4 inch per foot, or a 1:48 ratio.
Example 2: Find the fall needed for a target slope.
You want a 2 percent slope on a 50-foot run. Multiply the grade by the run:
Fall = (2 / 100) * 50 = 1 foot, which is 12 inches of drop across the run.
Frequently Asked Questions
What is the minimum slope for a drainage pipe?
There is no single minimum for every drainage pipe. The example size references above are 1/4, 1/8 and 1/16 inch per foot, equivalent to approximately 2.083333%, 1.041667% and 0.520833%. Confirm the adopted code, edition, amendments, service and any exception before choosing a required slope. Matching one selected numerical reference is not code approval.
What is the difference between slope, grade, and fall?
Fall is the raw vertical drop between the two ends of the pipe, measured in inches, feet, or millimeters. Slope is that fall spread over the horizontal run and written as a percent. Grade is the same ratio written as a plain decimal, so a fall of 1 foot over a 200-foot run is a fall of 1 foot, a slope of 0.5 percent, and a grade of 0.005 ft/ft. They describe one relationship in three formats, and pipe grades on plans are almost always labeled in percent.
How do you convert percent slope to inches per foot?
Divide the percent by 100 to get the grade, then multiply by 12, since there are 12 inches in a foot. A 2 percent slope is 0.02 times 12, or 0.24 inch per foot. Working the other way, the plumbing standard of 1/4 inch per foot is 0.25 divided by 12, which is 0.0208, or 2.08 percent. The calculator shows percent, inches per foot, decimal grade, ratio and angle together. It does not calculate flow velocity or establish a self-cleaning threshold.
