Channel Slope Calculator

Channel Slope Calculator that finds grade from drop and run, solves either one from a grade, and works out the bed slope a ditch, swale or a part-full pipe needs to carry the flow.

How the Channel Slope Calculator Works

The channel slope calculator has four modes. Grade from Drop and Run is the default, where you enter the vertical fall and horizontal length between two points on the channel bed. Drop from Grade and Run and Run from Grade and Drop solve the other two sides of the same triangle.

The fourth mode, Slope Needed for a Flow, turns the channel slope calculator into an open channel slope calculator built on Manning's equation. Enter the design flow, the channel shape, the flow depth and the lining, and it returns the bed slope that carries that flow at that depth. It also reports velocity, Froude number, critical slope and the shear the water puts on the lining.

Grade can be entered or read in six forms, as a percent, ft per ft, inches per foot, a 1 in X ratio, degrees or mm per meter. The options panel sets a starting elevation and station spacing, so the tool lists the bed elevation at every grade stake down the channel.

Slope Formula: Grade, Degrees and Ratio

Every slope starts as drop divided by run, using the same unit for both. Multiply by 100 for percent grade. A channel that falls 1.5 ft over 100 ft has a slope of 0.015 ft/ft, which is a 1.5% grade.

$$S=\frac{\text{Drop}}{\text{Run}}\text{Grade}=S\times 100$$

The angle comes from the arctangent of the slope, and the ratio form is its reciprocal. For the 1.5% channel, the angle is arctan(0.015) = 0.859° and the ratio is 1 / 0.015, or 1 in 66.7.

$$\theta =\arctan (S)\text{Ratio}=1\text{ in }\frac{1}{S}$$

Percent and degrees are not the same scale. A 100% grade rises one unit per unit of run, which is 45°, not 90°. At small grades the two run close to a straight line, with 1% near 0.57°, but they split apart fast on steep slopes.

Slope Conversion Chart

Most channel slope questions are a conversion between these forms. The chart gives each common grade as degrees, inches per foot, a 1 in X ratio, mm per meter and total fall over 10 ft. Every value comes from the formulas above.

Grade	Degrees	Inches per Foot	Ratio	mm per Meter	Fall Over 10 ft
0.5%	0.29°	0.06 in	1 in 200	5 mm	0.6 in
1%	0.57°	0.12 in	1 in 100	10 mm	1.2 in
1.5%	0.86°	0.18 in	1 in 66.7	15 mm	1.8 in
2%	1.15°	0.24 in	1 in 50	20 mm	2.4 in
2.5%	1.43°	0.30 in	1 in 40	25 mm	3.0 in
3%	1.72°	0.36 in	1 in 33.3	30 mm	3.6 in
4%	2.29°	0.48 in	1 in 25	40 mm	4.8 in
5%	2.86°	0.60 in	1 in 20	50 mm	6.0 in
8%	4.57°	0.96 in	1 in 12.5	80 mm	9.6 in
10%	5.71°	1.20 in	1 in 10	100 mm	12.0 in
12%	6.84°	1.44 in	1 in 8.33	120 mm	14.4 in
25%	14.04°	3.00 in	1 in 4	250 mm	30.0 in
33.3%	18.43°	4.00 in	1 in 3	333 mm	40.0 in
50%	26.57°	6.00 in	1 in 2	500 mm	60.0 in
57.7%	30.00°	6.93 in	1 in 1.73	577 mm	69.3 in
66.7%	33.69°	8.00 in	1 in 1.5	667 mm	80.0 in
100%	45.00°	12.00 in	1 in 1	1,000 mm	120.0 in

A ratio written as 1 in X means one unit of fall for X units of run, so 1 in 40 is 2.5%, 1 in 50 is 2% and 1 in 100 is 1%. Side slopes on ditch banks are usually written the other way, as horizontal to vertical, so a 1.5:1 bank is 66.7% and 33.7°.

Fall in Inches, Feet and Millimeters

To find total fall, multiply the grade as a decimal by the run. A 2% slope over 10 ft falls 0.02 × 120 in = 2.4 in, and over 12 ft it falls 2.88 in, a little under 3 in. Over 4 ft the same 2% gives 0.96 in, close to 1 in.

A 1% slope falls 0.01 ft for every foot of run, which is 0.12 in per foot or 1.2 in over 10 ft. That is also 1 ft of fall per 100 ft, the easiest way to picture it on a long ditch. A 5% slope falls 0.6 in per foot and 6 in over 10 ft.

In metric, the percent equals cm per meter, so 1% is 1 cm or 10 mm per meter and 2% is 2 cm or 20 mm per meter. The tool's mm per Meter option reads this directly, and it accepts fall and run in different units, such as fall in mm and run in meters.

The channel slope calculator also gives the fall over 25 ft and 50 ft, common lengths for swales and pipe runs. For drain lines, the Drainage Fall Calculator, Pipe Slope Calculator and Sewer Line Slope Calculator apply the plumbing code minimums.

Slope a Channel Needs for Its Flow

Grade from drop and run tells you what a channel has. Slope Needed for a Flow tells you what it needs. Manning's equation links flow, channel shape, lining roughness and slope, and the tool rearranges it to solve for slope in US units.

$$S={\left(\frac{nQ}{1.486A{R}^{2/3}}\right)}^2$$

Here Q is flow in cfs, n is Manning's roughness, A is the flow area in ft² and R is the hydraulic radius, A divided by the wetted perimeter P. In SI units with Q in m³/s and A in m², the 1.486 becomes 1.0. The channel slope calculator converts gpm and L/s for you, and 1 cfs equals about 448.8 gpm.

Take a trapezoidal ditch with a 2 ft bottom, 2:1 side slopes and 1 ft of water, carrying 10 cfs with n = 0.030. The flow area is 4 ft², the wetted perimeter is 6.47 ft and R is 0.618 ft. The slope needed is 0.484%, about 1 in 207, and the water moves at 2.5 ft/s.

Over a 500 ft ditch that grade means 2.42 ft of total fall. To check an existing channel instead, find its grade in the first mode and run the same section through the Manning's Flow Calculator to get its capacity.

Trapezoidal and Rectangular Channel Area

The shape sets A, P and the top width T. The channel slope calculator works these out, much like a trapezoidal channel area calculator, for a trapezoidal ditch, a rectangular channel, a V-shaped swale or a part-full circular pipe. Side slope z is the horizontal distance per 1 unit of vertical, with b as bottom width and y as flow depth.

Shape	Flow Area A	Wetted Perimeter P	Top Width T
Rectangular	b·y	b + 2y	b
Trapezoidal	(b + z·y)·y	b + 2y√(1 + z²)	b + 2z·y
Triangular (V)	z·y²	2y√(1 + z²)	2z·y
Circular, half full	πD²/8	πD/2	D

For a rectangular channel flow check, take a 3 ft wide concrete channel with 1 ft of water, a float finish (n = 0.015) and 12 cfs. Then A = 3 ft², P = 5 ft and R = 0.6 ft. The slope needed is 0.322%, the velocity is 4.0 ft/s, and the Froude number is 0.71, so the flow stays subcritical.

For a pipe that runs part full, pick Circular Pipe and enter the diameter. A 2 ft concrete pipe flowing half full with 5 cfs needs 0.195% slope. The Partial Pipe Flow Calculator covers other fill depths, and the Culvert Flow Calculator handles road crossings.

Manning's n for Channel Linings

Roughness has a large effect, since slope rises with n squared. Raising n from a smooth concrete 0.013 to a grassy 0.027 makes the needed slope about 4.3 times steeper for the same flow and depth. The presets in the channel slope calculator match the normal values from Chow's tables.

Lining	Minimum	Normal n	Maximum
Concrete, trowel finish	0.011	0.013	0.015
Concrete, float finish	0.013	0.015	0.016
Concrete, unfinished	0.014	0.017	0.020
Asphalt, smooth	0.013	0.013	0.013
Earth, clean, recently completed	0.016	0.018	0.020
Earth, clean, after weathering	0.018	0.022	0.025
Earth, gravel, clean	0.022	0.025	0.030
Earth, short grass, few weeds	0.022	0.027	0.033
Gravel bottom, riprap sides	0.023	0.033	0.036
Natural stream, clean, straight	0.025	0.030	0.033

These ranges come from Chow (1959), as reprinted by Oregon State University. Use the high end when a lining will grow weeds or collect debris between cleanings, since that is the condition the channel must still carry its flow in.

Froude Number, Critical Slope and Shear

The Froude number compares water speed with the speed of a surface wave. Below 1.0 the flow is subcritical, deep and calm, and above 1.0 it is supercritical, shallow and fast. The tool flags 0.8 to 1.2 as near critical, where the water surface turns wavy and unstable.

Critical slope is the grade at which the design flow would run at critical depth. In the trapezoidal example, critical depth is 0.72 ft and critical slope is 1.80%, so the 0.484% bed is a mild slope and the flow stays tranquil. A bed steeper than critical slope needs an erosion-resistant lining and will form a hydraulic jump where it flattens.

Shear stress is the drag the water puts on the lining, found as γ × R × S for the average and γ × y × S for the maximum on the bed. The trapezoidal ditch sees 0.187 lb/ft² on average and 0.302 lb/ft² at the deepest point. Compare that maximum with the permissible shear of the grass, stone or mat you plan to use.

Grading Next to a House

When a swale or yard grade runs beside a building, the codes set a minimum fall. IRC R401.3 requires the ground to fall at least 6 in within the first 10 ft from the foundation, which is a 5% slope, and paving within 10 ft must slope at least 2% away from the house.

The commercial code goes one step further. IBC 1804.4 also sets a 2% minimum for swales within 10 ft of the foundation. The channel slope calculator checks these rules on its fourth card and shows how much fall the first 10 ft still needs.

Roof water reaches these swales through gutters and downspouts. The Gutter Slope Calculator sets the gutter pitch, and the French Drain Calculator sizes a buried drain when there is no room for a surface swale.

Setting Grade Stakes

On site, a ditch is built from stakes marked with the bed elevation at fixed stations. Enter the upstream elevation and the station spacing in the options, and the channel slope calculator lists the bed elevation and the fall so far at every station down the channel.

With a start elevation of 250.00 ft and a 1.5% grade, each 10 ft station drops 0.15 ft. The bed reads 249.85 ft at 10 ft, 249.25 ft at 50 ft and 248.50 ft at 100 ft. A laser level or string line set to these marks keeps the bed on grade between stakes. The Download CSV for Excel button under the stake table saves the full list for a field sheet or a spreadsheet.

The sloped bed length is a touch longer than the horizontal run, 100.011 ft for that 100 ft run. The difference only matters on steep chutes, where it adds to lining and fabric quantities.

Channel Slope FAQs

These answers cover the slope questions people search most, with numbers you can check in the channel slope calculator.

What does a 2% slope look like?

A 2% slope falls about 1/4 in per foot, or 2.4 in over 10 ft and 2 ft over 100 ft. That is 1.15°, so it looks almost flat, yet water on a smooth surface runs off it steadily. It is the minimum code grade for paving and swales next to a house.

On a 4 ft wide patio, a 2% slope drops just under 1 in from the house side to the outer edge. A level held on the surface shows the bubble only slightly off center.

How do you calculate a 2.5 slope?

First decide what 2.5 means. A 2.5% grade falls 2.5 ft per 100 ft, which is 0.30 in per foot, 1 in 40 and 1.43°. A 2.5:1 side slope, common on ditch banks, means 2.5 ft across for each 1 ft down, which is 40% and 21.8°.

For a 2.5% channel over 80 ft, the fall is 0.025 × 80 = 2 ft. Enter the grade in the matching unit in the tool, percent for the first case and the 1 in X option for a ratio, and it converts the rest.

How do you calculate 1% slope per meter?

Multiply 1,000 mm by 0.01 to get 10 mm of fall per meter, which is the same as 1 cm per meter. Over 5 m a 1% slope falls 50 mm, and over 20 m it falls 200 mm.

The rule works for any grade, since the percent equals the cm of fall per meter. A 2% slope in meters falls 2 cm per meter, and a 0.5% slope falls 5 mm per meter.

What percentage is a 1.5 to 1 slope?

A 1.5:1 slope rises 1 unit for every 1.5 units across, so the grade is 1 / 1.5 × 100 = 66.7%. Its angle is arctan(0.667) = 33.7°.

A 2:1 bank is 50% and 26.6°, and a 3:1 bank is 33.3% and 18.4°. Enter the side slope as z in the trapezoidal shape, where 1.5 means 1.5 horizontal per 1 vertical.

What is a 30 degree slope as a percent?

Take the tangent of the angle and multiply by 100. The tangent of 30° is 0.577, so a 30° slope is a 57.7% grade, or about 1 in 1.73. It falls 6.93 in per foot and 69.3 in over 10 ft.

Pick Degrees as the grade unit in the channel slope calculator and it does this conversion directly. A 10% slope works the other way, as arctan(0.10) = 5.71°.

Can I do an open channel flow calculation in Excel?

Yes. Put the flow area and hydraulic radius in cells, then solve Manning's equation for slope. For the trapezoidal example, =(0.03*10/(1.486*4*0.618^(2/3)))^2 returns 0.00484, the 0.484% slope found above.

For flow instead of slope, use =1.486/n*A*R^(2/3)*SQRT(S). The step-by-step solution in the tool lists each value in order, and the stake table downloads as a CSV file that opens in Excel. For flow volumes over time, the Gallons Per Minute Calculator and Storm Water Runoff Calculator give the design flow to enter.