Pipe Grade and Slope Percent: Invert Stations and Rod Readings
Pipe has to hold grade between structures, and graded ground has to drain. Both come down to percent slope: how many feet the line rises or falls per 100 feet of run. This guide covers the slope math, shows how to turn a pipe slope into invert elevations and rod readings at each grade check, and then shows how to do it in the Grade Rod Calculator Slope tab. If you're new to rod readings and height of instrument, start with How to Read a Grade Rod.
Percent slope in plain terms
Slope % = rise ÷ run × 100
Rise is the change in elevation. Use a positive number when it goes up and a negative number when it goes down (fall).
Run is the horizontal distance.
Percent and ft/ft are the same thing written two ways. Divide the percent by 100 to get ft/ft:
0.50% = 0.005 ft/ft: 0.10 ft over 20 ft, 0.50 ft over 100 ft
1.00% = 0.01 ft/ft: 0.20 ft over 20 ft, 1.00 ft over 100 ft
2.00% = 0.02 ft/ft: 0.40 ft over 20 ft, 2.00 ft over 100 ft
Change in elevation = slope % ÷ 100 × distance
How slope changes the invert and the rod reading
The invert is the inside bottom of the pipe. That's the elevation the plans call out.
With the laser at one height (one HI), a rod reading goes down when the point goes up. So along a pipe run:
Rising pipe (+ slope): invert elevation goes up and the rod reading to the invert goes down.
Falling pipe (− slope): invert elevation goes down and the rod reading to the invert goes up.
At any distance along the run:
Invert elevation = start invert + (slope % ÷ 100 × distance)
Rod reading = start rod reading − (slope % ÷ 100 × distance)
The bedding or trench bottom is graded to the outside bottom of the pipe, which sits one wall thickness below the invert. Lower ground means a bigger rod reading, so:
Rod reading to outside bottom = invert rod reading + wall thickness (in feet; 4" = 0.333 ft)
Example 1: Pipe grade checks every 20 ft
A 100 ft run of pipe falling at 1.00%, with a grade check every 20 ft (a common pipe length).
Pipe run: 100 ft
Grade check interval: 20 ft
Slope: −1.00% (fall)
Start invert elevation: 95.00 ft
Start rod reading (to invert): 9.50 ft
Pipe wall thickness: 4" (0.333 ft)
The change per 20 ft is −1.00 ÷ 100 × 20 = −0.20 ft. Each station is 0.20 ft lower in elevation and 0.20 ft higher on the rod.
Station table (distance: invert elevation, rod reading to the invert, and rod reading with a 4" wall)
0 ft: invert 95.00, rod 9.50 (9' 6"), with 4" wall 9.83 (9' 10")
20 ft: invert 94.80, rod 9.70 (9' 8 3/8"), with 4" wall 10.03 (10' 3/8")
40 ft: invert 94.60, rod 9.90 (9' 10 3/4"), with 4" wall 10.23 (10' 2 3/4")
60 ft: invert 94.40, rod 10.10 (10' 1 1/4"), with 4" wall 10.43 (10' 5 1/4")
80 ft: invert 94.20, rod 10.30 (10' 3 5/8"), with 4" wall 10.63 (10' 7 5/8")
100 ft: invert 94.00, rod 10.50 (10' 6"), with 4" wall 10.83 (10' 10")
Feet-inch values are rounded to the nearest 1/8", as in the app screenshot below.
Check the arithmetic two ways:
End of run: 100 ft × 0.01 = 1.00 ft of fall. 95.00 − 1.00 = 94.00 invert, and 9.50 + 1.00 = 10.50 rod reading. ✓
Same laser line: invert + rod reading should equal the same number at every station. 95.00 + 9.50 = 94.80 + 9.70 = 94.00 + 10.50 = 104.50. ✓ (That's the HI from the grade rod guide example.)
Runs that don't divide evenly: if the same pipe were 110 ft long, you'd still check at 0, 20, 40, 60, 80 and 100. You'd also check the end of the run at 110 ft: invert 95.00 − 1.10 = 93.90, rod reading 9.50 + 1.10 = 10.60, and 10.93 with the 4" wall.
Example 2: Grading slope %
From rise and run. A swale should fall 1.00 ft over 50 ft:
Slope % = −1.00 ÷ 50 × 100 = −2.00%
From two rod readings. You don't need elevations, just two readings from the same laser setup and the distance between them:
Slope % = (rod 1 − rod 2) ÷ run × 100
Ground rises from point 1 to point 2: rod 1 = 5.20, rod 2 = 4.20, run 50 ft. (5.20 − 4.20) ÷ 50 × 100 = +2.00%
Ground falls from point 1 to point 2: rod 1 = 4.80, rod 2 = 5.30, run 25 ft. (4.80 − 5.30) ÷ 25 × 100 = −2.00%
Rod 1 is subtracted first because a smaller second reading means higher ground, which is a rise.
Quick reference
Slope % = rise ÷ run × 100 (ft/ft = slope % ÷ 100)
Slope % from rods = (rod 1 − rod 2) ÷ run × 100
Invert at distance = start invert + slope % ÷ 100 × distance
Rod at distance = start rod − slope % ÷ 100 × distance
Rod to outside bottom = invert rod + wall thickness (ft)
Doing it in Grade Rod Calculator
The Slope tab has two categories, Grading and Pipe, and each has two sub-modes.
Pipe, Rod Readings: rod readings at every station
Open the Slope tab and pick Pipe, then Rod Readings.
Enter Pipe Run (ft) 100, Grade Check Interval (ft) 20 and Slope % (+ rise / - fall) -1.
Enter Start Rod Reading 9.5. That's your reading on the invert at the start of the run.
Enter Pipe Thickness (in) 4. In Feet units, thickness is entered in inches (like 3" or 4 1/2) and the app converts it to feet. Pipe thickness is only in Rod Readings mode. The Elevation sub-mode doesn't have it.
The app lists every station with Rod Reading (Invert) and Rod Reading (+ Thickness): 9.50 / 9.83 ft at 0.00 ft, then 9.70 / 10.03, 9.90 / 10.23, 10.10 / 10.43 and 10.30 / 10.63, down to 10.50 / 10.83 ft at 100.00 ft. Each value has a feet-inch line under it, matching the Example 1 table. Use the + Thickness column when you're grading the trench bottom or bedding to the outside bottom of the pipe.
Pipe, Elevation: invert elevations at every station
Switch the sub-mode to Elevation and enter Pipe Run, Grade Check Interval, Start Invert Elevation and Slope %. There's no thickness field here. The app lists the Invert Level at each distance.
This screenshot uses a 25 ft interval: Pipe Run 100, Grade Check Interval 25, Start Invert Elevation 95, Slope -1. It shows 95.00, 94.75, 94.50, 94.25 and 94.00 ft at 0, 25, 50, 75 and 100 ft. With a 20 ft interval, you'd get the invert column from Example 1: 95.00, 94.80, 94.60, 94.40, 94.20 and 94.00.
Stations start at 0 and step by the interval, and the end of the run is always included, so a 110 ft run ends with a 110 ft row. On very long runs with a short interval, the app may limit how many rows it shows and tell you to use a larger interval.
Grading: slope % from rise and run, or from two rod readings
Pick Grading, then:
Rise mode: enter Run (ft) and Rise (ft) on each row, and the app shows Slope (%) = Rise ÷ Run × 100. Run 50 with Rise -1 shows -2.00. Rise also accepts feet-inch entries, including negatives like -6" or -0'6".
Rod Readings mode: enter Rod 1, Rod 2 and Run (ft) on each row, and the app shows Slope (%) = (Rod 1 − Rod 2) ÷ Run × 100. Rod 5.2 to 4.2 over 50 shows 2.00, and 4.8 to 5.3 over 25 shows -2.00.
You can check up to 5 rows at once. + adds a row and × removes the last row that has entries. Slope % shows to the number of decimal places set in Settings (1–5).
Clear All resets the pipe inputs and the grading rows.
The app works offline and has no ads. It's a yearly subscription: $1.99/year after a 14-day free trial. The store shows the current price where you are.
More on the app: Grade Rod Calculator page · Reading the rod and HI: How to Read a Grade Rod
FAQ
What does "Move Laser to Higher Location" mean? The app shows this red warning when a calculated rod reading comes out negative. A negative reading means the point is above your instrument line, so the laser can't hit the rod there. Set the laser up higher, shoot the benchmark again, and enter the new reading.
In the Elevations tab, with the same control (100 and 4.5, so HI 104.50), an elevation of 105 gives 4.50 − (105 − 100) = −0.50 ft (−6"), shown in red with the warning.
In the Basic tab, the same thing happens with Add Measurement. Initial Rod Reading 2.50, plus 3.20 up: 2.50 − 3.20 = −0.70 ft (−8 3/8"), with the warning.
Does the app tell me cut or fill? Not directly. It gives you the target rod reading (Elevations tab, Elevation Mode), the elevation for a reading (Rod Reading Mode), or the rise or fall between two readings (Basic tab). Cut or fill is the difference between that and your ground reading, as shown above. In this guide, actual reading minus grade rod: positive is fill, negative is cut. Some crews subtract the other way and flip the labels, so pick one convention and use it across the crew.
Decimal rod or feet-and-inches? Either works. Grade Rod Calculator accepts decimal feet and feet-inch entries like 5'8 1/2". In Feet units it shows both decimal and feet-inch results, so you can match the rod in your hand.
Does switching to Meters convert my numbers? No. Feet or Meters is a display label only. Enter your values in the units you're using. In Meters, the feet-inches line is hidden.
Where do I get the app? On Google Play for Android and the App Store for iPhone and iPad. More details are on the Grade Rod Calculator page.
About Us
Linesite Tech specializes in innovative mobile and web applications for the construction industry.
