What this calculator does
A pipe is a hollow cylinder, so this calculator runs the same geometry every cylinder volume problem runs: volume equals pi times radius squared times length. Feed it inner diameter and length in whatever unit you measured in, get the answer back in gallons or liters. No email, no signup.
This number gets used more often than it looks like it should on paper: filling a hydronic loop, dosing a chemical treatment by volume, or checking how much water sits in a long recirc line before a job starts. Get the diameter wrong, using the outer measurement or the nominal size instead of the actual bore, and every number downstream of it is wrong too.
How the math works
A pipe is a hollow cylinder, so its volume follows the same formula as any cylinder: multiply pi by the radius squared, then multiply by the length.
V = π × r² × L
Radius is half the diameter, not the diameter itself. Plug the diameter straight into the formula in place of the radius and the volume comes out four times too high, since r² scales as the square of whatever number goes in.
The diameter that matters is the pipe's inner diameter (ID), the actual bore water or refrigerant moves through, not the outer diameter (OD) or the nominal size printed on the label. A pipe stamped "1 inch" rarely has a 1-inch bore once wall thickness is subtracted. Schedule 40 PVC, copper, and PEX each shave a different amount off nominal size, so measuring the actual ID, or pulling it from the manufacturer's spec sheet, is the step that keeps the rest of the math honest.
Running the formula gives a result in cubic units first: cubic inches if you measured in inches, cubic millimeters if you measured in millimeters. Getting to gallons or liters from there is a second step, a straight unit conversion, not a different formula:
- 1 US gallon = 231 cubic inches
- 1 liter = 61.02 cubic inches, or 1,000,000 cubic millimeters
The calculator above runs both steps at once. Enter diameter and length in inches, feet, centimeters, or millimeters, whatever you actually measured in, choose gallons or liters for the result, and it handles the geometry and the conversion together.
Worked example
Say you're refilling a hydronic baseboard loop and need to know how much water it takes to fill 40 feet of 3/4-inch inner diameter copper line before dosing inhibitor into it.
Step 1. Radius: 0.75 in ÷ 2 = 0.375 in
Step 2. Length in inches: 40 ft × 12 = 480 in
Step 3. Cylinder formula: V = π × 0.375² × 480 = π × 0.140625 × 480 ≈ 212.06 in³
Step 4. Cubic inches to gallons: 212.06 ÷ 231 ≈ 0.92 gallons
That loop holds about 0.92 gallons before a single fitting or elbow goes in, useful for both the fill volume and for figuring out how much chemical inhibitor a system that size needs.
The same formula holds in any unit. Run it in metric instead, a 20 mm inner diameter line, 10 meters long (enter it as 1,000 cm), and the geometry works out to almost exactly 3.14 liters. That's a coincidence of this specific diameter and length, not a rule, but a good way to check that a calculator handling metric input is actually converting units correctly instead of quietly assuming inches.
Pipe volume by diameter (gallons per foot)
Once you have run the formula a few times, this table saves the arithmetic for common inner diameters. Multiply the gallons-per-foot figure by the run's actual length to get total volume.
| Inner diameter | Gallons per foot |
|---|
| 1/2 in | 0.010 |
| 3/4 in | 0.023 |
| 1 in | 0.041 |
| 1 1/4 in | 0.064 |
| 1 1/2 in | 0.092 |
| 2 in | 0.163 |
| 3 in | 0.367 |
| 4 in | 0.653 |
| 6 in | 1.469 |
These numbers come straight from the cylinder formula above (π × r² × 12 in, divided by 231), not a separate lookup table. Measure the actual inner diameter, not the nominal size, before using this for anything you're dosing or filling.
Why pipe volume matters on the job
Three situations come up on almost every job where this number changes what happens next.
Flushing a new or repaired line
A hydronic loop, radiant floor system, or newly installed water line typically gets flushed before it goes into permanent service, clearing out flux residue, debris, and trapped air. Trade practice ties flush volume to a multiple of the pipe's own volume rather than a fixed number of minutes, so if the underlying pipe volume is off, the flush comes up short and the line goes into service still carrying what should have come out.
Dosing chemicals by volume
Boiler inhibitor, glycol, and disinfection chemicals for a new potable line all get dosed against system volume, not pipe length. A rate printed on a product label as ounces per gallon only lands correctly if the gallon figure feeding it is correct. Running the pipe volume first, then applying the label's dosing rate, replaces a guess with an actual number.
Sizing checks on water heaters and line sets
A tank or tankless water heater sits behind some length of supply and recirc piping, and that piping holds water that has to move or reheat before the fixture at the far end sees the temperature the heater is set to. Knowing the volume of a long recirc run can explain a slow hot-water complaint that has nothing wrong with the heater itself, and the same math covers how much refrigerant a line set holds before a job starts. For how fast that volume moves rather than how much it holds, see the flow rate calculator.
