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Circulator pump size calculator
A circulator is chosen by two numbers, the flow it has to move and the head it has to make at that flow. The load and the temperature drop give the GPM, and the length of the circuit, with the fittings and the devices in it, gives the head. Caleffi's worked circuit has 100.2 ft of equivalent length in 3/4 inch Type M copper. At 5 GPM (50,000 BTU/h at a 20°F drop) this page gives 5.37 ft of head, 2.32 psi across the pump, at 3.10 ft/s. Caleffi's own formula for 140°F water gives 4.93 ft, and the page reads about 9 percent higher at that flow, because the two formulas use different flow exponents and this page uses one Hazen-Williams friction for every water temperature. The page works in water only. To pick the tube size first, use the hydronic pipe size calculator. To size the boiler that feeds the loop, use the boiler size calculator.
- Take the circuit load in BTU/h from the heat loss or the emitter rating, and choose the design temperature drop. Caleffi calls 20°F the traditional value.
- Choose the copper tube type and size, the measured length of tube, and the number of elbows, tees and check valves. Add any other equivalent length and the head loss of the boiler, emitters and valves from their makers' data.
- The result gives the GPM, the head in feet and the pressure rise in psi. Find the GPM on the pump curve and check that the head there is at or above the required head, with the crossing in the middle third of the curve.
Example result for the default inputs
50,000 BTU/h at 20°F drop through 100.2 ft equivalent of 3/4 inch Type M.
Required flow
5.00 GPM
Required head
5.37 ft of head
Pressure rise
2.32 psi
Tube velocity
3.10 ft/s
| Load | 50,000 BTU/h |
|---|---|
| Temperature drop | 20°F |
| Tube | 3/4 inch Type M, inside diameter 0.811 inch |
| Straight tube | 58.0 ft |
| Fittings counted | 17.0 ft equivalent |
| Other equivalent length | 25.2 ft |
| Total equivalent length | 100.2 ft |
| Friction | 0.0232 psi per ft, 5.35 ft of head per 100 ft |
| Head of tube and fittings | 5.37 ft |
| Head of devices | 0.00 ft |
| On the pump curve | At least 5.37 ft of head at 5.00 GPM, with the crossing of the pump curve and the system curve in the middle third of the pump curve |
| Tube head at 50 percent of flow | 2.50 GPM, 1.49 ft, 1.55 ft/s |
| Tube head at 75 percent of flow | 3.75 GPM, 3.15 ft, 2.33 ft/s |
| Tube head at 100 percent of flow | 5.00 GPM, 5.37 ft, 3.10 ft/s |
| Tube head at 125 percent of flow | 6.25 GPM, 8.11 ft, 3.88 ft/s |
| Tube head at 150 percent of flow | 7.50 GPM, 11.36 ft, 4.65 ft/s |
- Water only. The 500 in the flow formula, the density and the friction all change with antifreeze, so a glycol loop needs the fluid maker's data for both the flow and the head.
- Friction is the Hazen-Williams figure that the Copper Tube Handbook uses, and it does not change with water temperature. Next to Caleffi's 140F formula it can read higher or lower, depending on the flow: higher at larger flows, and lower at small flows, by 10 to 20 percent at a few tenths of a GPM and more below that. Water colder than 140F loses more than the 140F formula gives, so allow margin at small flows and with cool water.
- No head loss was entered for the boiler, the heat emitters, the valves or any other device, so the head above is the tube and fittings only. Take their loss from each maker's data at this flow and add it.
- In a closed loop that is full and purged of air, the circulator replaces friction only. Caleffi notes that it does not lift the water, so the height of the building is not added.
- If the water routinely runs hotter than 140°F, the Copper Tube Handbook asks for 2 to 3 ft/s, and this tube runs at 3.10 ft/s.
For estimation purposes only. Consult a licensed engineer for final designs.
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How the pump flow and head are calculated
A circulator in a closed loop has one job, which is to replace the head the water loses to friction as it goes round. This page turns a load in BTU/h and a design drop into the flow in GPM, adds up the equivalent length of the tube, the fittings and the valves in the circuit, and turns that length into the head in feet that the pump has to make at that flow. It also lists the head of the tube at other flows, so a pump curve can be read against more than one point. Input is a tube you have already chosen, in Type L or Type M copper. The tube size itself comes from the hydronic pipe size calculator, and antifreeze is out of scope.
- Flow
GPM = load / (500 x temperature drop)The 500 is the 8.33 pounds in a gallon of water times 60 minutes. 50,000 BTU/h at a 20°F drop is 5 GPM, which Caleffi's example circuit carries. It fits cold water best, so hotter water needs a little more flow.- Equivalent length
L = straight tube + fittings from Table 14.7 + other lengthThe Copper Tube Handbook gives each fitting as the feet of straight tube that lose the same head. In 3/4 inch tube a standard 90 degree elbow is 2 ft, a tee through the side branch is 3 ft and a check valve is 3 ft, the same lengths as Caleffi's tally. The default circuit has 58 ft of tube, 17 ft of counted fittings and 25.2 ft of other length, which is 100.2 ft.- Friction
psi per ft = 4.52 x GPM^1.85 / (150^1.85 x inside diameter^4.87)The Hazen-Williams formula that the handbook says its Table 14.6 is based on, with C = 150, and the exact bore of the tube. At 5.00 GPM a 3/4 inch Type M tube, bore 0.811 inch, loses 0.0232 psi per foot, or 5.35 ft of head per 100 ft, and runs at 3.10 ft/s.- Head of the circuit
head ft = friction x L x 144 / 62.4 + device headOver 100.2 ft the tube and fittings lose 5.37 ft of head. Devices such as the boiler and the emitters add their own loss, which comes from their makers' data at the design flow and is added as entered.- Pressure rise
psi = head / (144 / 62.4)Caleffi's Formula 4-1 turns head into pressure with the density of the water, so 1 psi is 2.31 ft of head. 5.37 ft of head is 2.32 psi across the pump, which is what a pair of gauges on the pump reads.- Head at other flows
head at q = head at design x (q / design flow)^1.85The friction formula has the flow to the power 1.85, so the head of the tube falls to 1.49 ft at 2.50 GPM and climbs to 11.36 ft at 7.50 GPM, 2.1 times the design head. Five points are listed in the result, from 50 to 150 percent of the flow.- Reading the pump curve
pump head at the design GPM >= required headFind the design GPM on the horizontal axis of a pump curve and read the head up to the curve. It has to be at or above the required head, and Caleffi suggests that the crossing of the pump curve and the circuit's own head loss curve fall in the middle third of the pump curve.
Worked examples from published hydronic data
The default case is the circuit of Figures 4-5 to 4-7 in Caleffi's idronics 16. Its tally is 58 ft of tube, 4 elbows, 2 side-branch tees and 1 check valve, which the handbook's Table 14.7 gives as 17 ft, and 25.2 ft of run tees, ball valves and a globe valve that the table has no figure for. The total is 100.2 ft. Caleffi's formula gives 4.93 ft of head at 5 GPM with 140°F water, and this page gives 5.37 ft with the cold water friction of the handbook.
The table below sets the 6 printed points of Caleffi's head loss curve, 0.295 x GPM^1.75, next to its Formula 4-2 and next to this page's head for the same circuit. Caleffi's formula reproduces its printed points. This page's column is higher at each flow above 2 GPM, and the gap grows with the flow because the Hazen-Williams exponent is 1.85. The head falls to 1.49 ft at 2.50 GPM and rises to 11.36 ft at 7.50 GPM.
| GPM | Printed, ft of head | Formula 4-2, ft | This page, ft | Formula agrees |
|---|---|---|---|---|
| 2 | 0.99 | 0.99 | 0.98 | Yes |
| 4 | 3.34 | 3.34 | 3.55 | Yes |
| 6 | 6.79 | 6.78 | 7.52 | Yes |
| 8 | 11.2 | 11.22 | 12.80 | Yes |
| 10 | 16.6 | 16.58 | 19.34 | Yes |
| 12 | 22.8 | 22.81 | 27.10 | Yes |
Eight cases below run through the same functions the form uses. Five of them share the 50,000 BTU/h load and change one input at a time. In Type L the head is 6.29 ft, with 3 ft of boiler loss it is 8.37 ft, and in 1 inch tube it falls to 1.59 ft. A small zone, a boiler loop and a light commercial loop show how the head grows with the length and the devices.
| Case | Setup | Result |
|---|---|---|
| Caleffi circuit, Type M | 50,000 BTU/h, 20°F drop, 3/4 inch Type M, 100.2 ft equivalent | 5.00 GPM, 5.37 ft of head, 2.32 psi, 3.10 ft/s |
| Same circuit in Type L | 50,000 BTU/h, 20°F drop, 3/4 inch Type L, 100.2 ft equivalent | 5.00 GPM, 6.29 ft of head, 2.72 psi, 3.31 ft/s |
| Same circuit with a 3 ft boiler loss | 50,000 BTU/h, 20°F drop, 3/4 inch Type M, 100.2 ft equivalent, 3 ft of device head | 5.00 GPM, 8.37 ft of head, 3.62 psi, 3.10 ft/s |
| Same circuit in 1 inch tube | 50,000 BTU/h, 20°F drop, 1 inch Type M, 106.7 ft equivalent | 5.00 GPM, 1.59 ft of head, 0.69 psi, 1.83 ft/s |
| Same load at a 10°F drop, 1 inch tube | 50,000 BTU/h, 10°F drop, 1 inch Type M, 106.7 ft equivalent | 10.00 GPM, 5.72 ft of head, 2.48 psi, 3.67 ft/s |
| Small zone, 25,000 BTU/h | 25,000 BTU/h, 20°F drop, 1/2 inch Type M, 48.0 ft equivalent | 2.50 GPM, 4.00 ft of head, 1.74 psi, 3.15 ft/s |
| Boiler loop, 150,000 BTU/h | 150,000 BTU/h, 20°F drop, 1-1/4 inch Type M, 171.5 ft equivalent, 4 ft of device head | 15.00 GPM, 11.28 ft of head, 4.89 psi, 3.67 ft/s |
| Light commercial loop, 600,000 BTU/h | 600,000 BTU/h, 20°F drop, 2-1/2 inch Type M, 361.5 ft equivalent, 6 ft of device head | 60.00 GPM, 14.06 ft of head, 6.09 psi, 3.93 ft/s |
Standards and data sources
- Copper Development Association, Copper Tube Handbook (CDA Publication A4015-26/24) - Table 14.7 for the equivalent length of elbows, tees and check valves in 1/2 inch to 6 inch tube, with its note that threaded fittings take double and that the lengths rest on C = 150 in the Hazen-Williams formula. Page 15 gives the water velocity limits of 8 ft/s for cold water and 5 ft/s for hot water up to about 140°F, and Table 14.6 the friction loss.
- Caleffi, idronics issue 16, Circulation in hydronic systems - Section 4 for the head of a circuit, with the worked circuit of 100.2 ft of equivalent length that this page opens on, its head loss curve and Formula 4-1 for head and pressure. Pump curves, the operating point and the guideline to select a circulator so that the crossing falls in the middle third of the curve are in section 5. It also quotes an ASHRAE guideline of 4 ft/s for tube 2 inch and smaller and 4 ft of head per 100 ft above that.
- Caleffi, idronics issue 31, Appendix B, Pressure drop for copper tubing - The Hazen-Williams formula for copper tube in psi per foot and its worked example of 150 ft of 3/4 inch Type L at 6 GPM, which the tests of the hydronic pipe size calculator reproduce.
Limitations of this calculator
- Water only. Antifreeze changes the 500 in the flow formula, the density and the friction, and Caleffi says its fuller formula, with the fluid's own density and specific heat, should be used for a glycol solution. Glycol needs the fluid maker's data for both the flow and the head.
- The friction is one Hazen-Williams figure for every water temperature. On Caleffi's 100.2 ft circuit at 5 GPM with 140°F water, its own formula gives 4.93 ft of head and this page gives 5.37 ft, about 9 percent more. The page takes the same friction at every water temperature. Whether the page reads above or below Caleffi's formula depends on the flow: in that same 3/4 inch Type M circuit it is about even at 2 GPM, 17 percent more at 10 GPM and 14 percent less at 0.5 GPM. Water colder than 140°F loses more than Caleffi's 140°F formula gives, so allow margin at small flows and for a cool loop such as a heat pump or radiant floor circuit.
- Copper only. Type L and Type M from 1/2 inch to 6 inch are in the tables. PEX, Type K copper, steel and plastic pipe have other bores and other friction and are not included. Caleffi says its smooth-tube formula should not be used for iron or steel piping, which needs the Darcy-Weisbach formula and the pipe's roughness.
- One tube size around the loop. The page treats the circuit as a single series run of the size you pick. A circuit that steps down in size, or a loop with parallel zones, needs each section worked on its own and the heads added in series or combined by flow.
- Five fitting types. Table 14.7 also lists couplings and ball, gate and butterfly valves, and the page leaves them to the other equivalent length field, which takes up to 10,000 ft. The handbook's allowances are for smooth-bore soldered fittings, and threaded fittings take double.
- Devices are entered, not calculated. The boiler, the heat emitters and any control valve lose head that depends on the product, and the field takes up to 500 ft of head at the design flow from the maker's data. That figure is not scaled to other flows, so the list of heads at other flows is the tube and fittings only.
- No safety margin is added. The result is the head at the design flow, and a margin for fouling, uncertain lengths or later additions is the designer's call.
- The page does not choose a pump. It gives the flow and the head to look for, and the pump maker's curve, the efficiency, the motor and the electrical details decide the model. A closed loop that is full and purged of air is assumed, which is the case where the circulator replaces friction only.
- This is a planning estimate, not a design drawing. A licensed contractor or engineer, the manufacturer's data and the authority having jurisdiction decide the installation.
Common circulator sizing mistakes
- Adding the height of the building to the head. Caleffi explains that in a closed circuit that is full of water, the circulator is only responsible for replacing the head lost to friction and does not lift the fluid up the rising pipe. The head that matters is the 5.37 ft of friction in the default circuit and any device loss, with no allowance for floors. An open system or a tank that the water is lifted into is a different problem.
- Counting only the straight tube. The 58 ft of tube in the default circuit loses 3.11 ft of head on its own. With 17 ft of counted elbows, tees and a check valve and 25.2 ft of valves and tees from Caleffi's tally, the circuit is 100.2 ft long for friction and loses 5.37 ft. The handbook says that for close estimates an allowance has to be added for valves and fittings.
- Leaving the boiler and emitters out of the head. The tube figures stop at the tube. A boiler that loses 3 ft of head at 5 GPM takes the requirement from 5.37 ft to 8.37 ft and the pressure rise from 2.32 psi to 3.62 psi. Their loss comes from each maker's data at the design flow.
- Reading the pump's maximum head, not its head at your flow. A circulator adds less head as the flow rises, which Caleffi shows with the pump curve. The number that counts is the head the curve gives at the design GPM, which has to be at or above 5.37 ft at 5.00 GPM here. Because the friction head climbs with the flow to the power 1.85, the tube of the default circuit loses 11.36 ft at 7.50 GPM, 2.1 times the design head, so a pump that only just reaches the design point has little to give if the flow is wrong.
- Taking the drop from the wrong circuit. Each circuit gets its own drop. In 1 inch tube the same 50,000 BTU/h needs 5.00 GPM at 20°F and loses 1.59 ft over 106.7 ft of equivalent length. At 10°F it needs 10.00 GPM and loses 5.72 ft, and the head is about 3.6 times higher for double the flow. Caleffi gives 10 to 15°F for radiant floor circuits and 25 to 35°F for panel radiators and fan coils.
- Using these figures for another pipe material. The bores and the friction on this page are for Type L and Type M copper. In Type L the default circuit runs at 3.31 ft/s and needs 6.29 ft of head, 17 percent more than Type M, from the smaller bore alone. PEX, steel and plastic pipe differ more than that, so take their head loss from the pipe maker's tables.
Common questions about circulator pump size
How do you find the GPM for a circulator pump?
Divide the load in BTU/h by 500 times the temperature drop in °F. The 500 is 8.33 pounds per gallon times 60 minutes per hour. 50,000 BTU/h at a 20°F drop is 5 GPM, and the same load at 10°F is 10.00 GPM. The factor fits cold water best, so a hot loop needs a little more flow.
How do you find the head a circulator has to overcome?
Add up the equivalent length of the circuit, which is the straight tube plus the length each fitting and valve is worth, and apply the friction loss of the tube at the design flow. Caleffi's circuit of 100.2 ft at 5 GPM in 3/4 inch Type M copper gives 5.37 ft of head on this page. Add the head loss of the boiler, the emitters and the valves from their makers' data.
What do I look for on the pump curve?
Find the design flow on the GPM axis and read up to the curve. The head there has to be at or above the required head, 5.37 ft at 5.00 GPM in the default case. Caleffi suggests selecting the circulator so that the crossing of its pump curve and the circuit's head loss curve falls in the middle third of the pump curve, where the wire-to-water efficiency is better than at either end.
Does the height of the building add head?
No, in a closed loop that is full of water and purged of air. Caleffi explains that the circulator is only responsible for replacing the head lost to friction, and that it does not lift the fluid up the rising side of the circuit. That is why a small circulator can serve a loop that rises several stories.
How much head do fittings add?
The Copper Tube Handbook gives each fitting as an equivalent length of tube in its Table 14.7. In 3/4 inch tube a standard 90 degree elbow is 2 ft, a tee through the side branch is 3 ft and a check valve is 3 ft. The allowances are for soldered fittings, and threaded fittings take double. Fittings in the default circuit add 17 ft of equivalent length.
Why is the head higher than Caleffi's example?
Caleffi's formula for its 100.2 ft circuit is for 140°F water and gives 4.93 ft at 5 GPM. This page uses the Hazen-Williams formula with C = 150, the one in the Copper Tube Handbook, with no change for water temperature, and gives 5.37 ft, about 9 percent more. The gap depends on the flow. In that circuit the page reads 17 percent more at 10 GPM, about even at 2 GPM and 14 percent less at 0.5 GPM, because the two formulas use different flow exponents. Water colder than 140°F loses more than the 140°F formula gives.
Should I add a safety factor to the head?
The page adds none, because the sources it quotes give no factor for it. What it shows is the friction at the design flow for the lengths and devices you enter. A margin for uncertain lengths, fouling or later additions is a decision for the designer, and it is better made on the lengths than as a percentage on the final head.
Can I use it for a glycol loop, PEX or steel pipe?
No. The 500 in the flow formula and the friction both assume water, and the bores and friction are for copper. Caleffi says its fuller formula, with the density and specific heat of the fluid, should be used for an antifreeze solution, and that its smooth-tube formula is not for iron or steel pipe. Get the fluid maker's and the pipe maker's data for those.
What if the pipe size is not chosen yet?
Use the hydronic pipe size calculator to pick the smallest copper tube under a velocity limit, then enter that size here. Caleffi quotes an ASHRAE guideline of 4 ft/s for tube 2 inch and smaller. A larger tube cuts the head, and in 1 inch tube the default circuit needs 1.59 ft against 5.37 ft, though it then runs at 1.83 ft/s, under the 2 ft/s that Caleffi gives for carrying air to the separator.
Is there a limit on how many times I can run this?
No. This calculator runs in your browser with no daily limit and no signup.
Used on the same job
Find the duty point, then read the pump curve
The flow and the head here are the point the pump has to reach. Take the maker's pump curve, find the flow on the horizontal axis and check the head at or above the required head, with the crossing of the pump curve and the circuit's own head loss curve in the middle third of the pump curve. The tube comes from the hydronic pipe size calculator, and the boiler output from the boiler size calculator. You can also ask the assistant to go over a pump selection.
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