Pump Power and Energy Cost Calculator

From flow and head to an electricity bill

A pump turns electrical power into flow and pressure, and loses some of it on the way. The useful part is the hydraulic power:

With ρ = 1000 kg/m³, g = 9.81 m/s², Q in m³/s and H in metres, P_hyd comes out in watts. Divide by the pump and motor efficiencies to get what the motor draws from the grid, then multiply by the hours it runs.

Take a pump moving 120 m³/h against 32 m of head with 72% pump efficiency and a 94% efficient motor. Hydraulic power is about 10.5 kW, the motor draws about 15.5 kW, and over 6,000 hours a year that is roughly 92,800 kWh. At 0.12 per kWh, around 11,100 a year, for one pump. Over a 15-year life the electricity typically costs many times the purchase price of the pump, which is why efficiency at the real operating point matters more than the price tag.

Why throttling wastes energy

Most systems do not need full flow all year. Heating demand changes with the weather, process demand with production. The traditional way to cut flow is a throttling valve: the pump keeps running at full speed and the valve burns off the extra pressure. Power falls only a little, because the pump moves along its curve to a point with less flow but more head.

A variable speed drive does the opposite. It slows the pump down so that it produces only the flow and head the system needs. By the affinity laws, flow falls in proportion to speed, head with the square of speed, and power with the cube. Halving the speed cuts the power to about an eighth, at least in a system with no static head.

The catch: static head

The cube law only holds when all of the head is friction. If the pump must also lift water to a height or push against a fixed pressure, that part does not shrink when the flow drops, and the savings shrink with it. This is why the calculator asks for the static head share. A closed heating or chilled water loop has almost none, so variable speed pays off handsomely. A pump lifting water 30 m to a reservoir with little pipe friction may save very little.

How the part-load estimate is made

For each flow step the calculator estimates two powers. With throttling, it uses a typical shape for a centrifugal pump power curve, roughly P/P_design ≈ 0.45 + 0.55 · Q/Q_design. With a variable speed drive, it follows the system curve, H = H_static + H_friction · (Q/Q_design)², assumes the pump efficiency stays roughly constant and adds about 3% for drive losses. Both are approximations. Real pump efficiency usually drops a little at low speed, so treat the saving as a good first estimate for deciding whether a drive is worth a proper study, not as a guaranteed figure.

Pumps in a heating network are moving water that you sized with the heating flow rate calculator and pushing it through pipes whose losses the pressure drop calculator gives you. Those two numbers are exactly the flow and head this calculator needs.

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Frequently asked questions

Where do I find the pump efficiency?

On the pump curve from the manufacturer, at your actual flow and head, not at the best efficiency point printed in the brochure. Many pumps run well away from their best point, and efficiency there can be 10 to 20 percentage points lower. If you have no curve, 60 to 75 percent is a common range for medium-size centrifugal pumps.

How do I convert pressure to head?

For water, 1 bar is about 10.2 m of head and 1 psi about 2.31 ft. The calculator converts automatically when you choose bar, kPa, ft or psi.

Is a VFD always worth it?

No. It pays off when the flow really varies and most of the head is friction, as in closed heating and cooling loops. For pumps that run at constant full load, or systems dominated by static lift, the saving can be small. A drive also adds its own losses of a few percent and some cost for harmonics filtering and maintenance.

Why does the calculator use water density of 1000 kg/m³?

It is accurate to within a few percent for water between about 0 and 90 °C. For hot water near 90 °C the true density is about 965 kg/m³, which lowers the power by roughly 3 percent.