In short: pump power scales with the cube of speed, so slowing a pump saves far more energy than the speed reduction alone suggests. Dropping a 5 HP pump to 70% speed cuts power draw to about 34% of full — running 4,000 hours a year at $0.15/kWh, that's roughly $1,470 saved annually. Use the calculator above for your own pump and runtime.
These figures are planning estimates based on the pump affinity laws. Actual savings depend on your specific pump curve and system — verify with pump performance data for critical decisions.
How to calculate variable-speed pump savings
The pump affinity laws describe how flow, head and power change as a centrifugal pump's speed changes. Power is the one that matters for savings, because it follows a cube relationship:
Worked example. A 5 HP pump (3.729 kW) slowed to 70% speed: power ratio = 0.70³ = 0.343, so reduced power = 3.729 × 0.343 = 1.279 kW — a saving of 2.450 kW. Running 4,000 hours a year at $0.15/kWh, energy saved is 2.450 × 4,000 = 9,798 kWh, worth $1,470 — the calculator's default result.
Why this beats throttling. A valve-throttled pump still spins at full speed and draws close to full power regardless of how much the valve restricts flow — the excess energy just turns into heat and noise at the valve. A VFD instead reduces the power the motor draws at the source, which is why the cube-law savings are real and not just moved elsewhere in the system.
Why speed, power and runtime change the answer
Speed reduction has an outsized effect. Because power follows the cube of speed, a 20% speed cut (to 80%) reduces power by about 49%, and a 50% speed cut reduces power by nearly 88% — the savings curve steepens fast as speed drops.
Flow and head don't fall nearly as much. Flow scales linearly with speed (80% speed gives 80% flow) and head scales with speed squared (80% speed gives 64% head) — both far gentler reductions than the cube law applied to power. This is exactly why VFDs are such an effective energy-saving technology: a modest, often barely noticeable, service reduction buys a large energy saving.
Runtime and rate scale savings linearly. Double the annual operating hours or the electricity rate, and the dollar savings simply double — the cube-law leverage is entirely in the speed ratio itself. See the pump affinity laws calculator to explore all three relationships (flow, head and power) without the cost conversion.
Reference: power & cost savings by speed reduction
Percent reduction in power draw (and therefore energy cost) at common speed setpoints — independent of pump size.
| Speed | Power vs. full | Savings |
|---|---|---|
| 95% | 85.7% | 14.3% |
| 90% | 72.9% | 27.1% |
| 80% | 51.2% | 48.8% |
| 70% (default) | 34.3% | 65.7% |
| 60% | 21.6% | 78.4% |
| 50% | 12.5% | 87.5% |
Worked examples
5 HP pump, 70% speed
$1,470/year
4,000 hrs/year at $0.15/kWh — the calculator's default. A 65.7% cut in energy cost from a 30% speed reduction.
Same pump, gentle 90% trim
$606/year
Just a 10% speed cut still saves about 27% of energy cost — useful where flow can only be trimmed slightly.
10 HP pump, deep 50% cut
$3,915/year
A larger pump running at half speed saves 87.5% of its energy cost — common for oversized pumps that spend most of their time at partial load.
What this calculator doesn't include
VFD hardware and installation cost. This tool estimates ongoing energy savings only. Compare the annual figure against a VFD's installed cost to work out a simple payback period.
Motor and drive efficiency changes. Real motors and VFDs have their own efficiency curves that vary somewhat with load and speed; this calculator applies the ideal affinity relationship to your measured or nameplate power draw.
System curve effects at very low speed. Near a pump's minimum flow, the affinity laws become less accurate. For sizing a specific VFD application, check the pump's published performance curve or consult the pump affinity laws calculator alongside manufacturer data.
Frequently asked questions
How does a variable-speed pump save energy?
A variable frequency drive (VFD) slows the pump motor down instead of running it at full speed and throttling the excess flow with a valve. Because pump power scales with the cube of speed, even a modest speed reduction cuts power draw disproportionately — running at 80% speed uses only about 51% of full-speed power, not 80%.
What is the pump affinity cube law?
The affinity laws describe how a pump's flow, head and power change with speed: flow scales linearly with speed, head scales with speed squared, and power scales with speed cubed. The cube relationship for power is what makes speed reduction such an effective energy-saving strategy — small speed cuts produce large power cuts.
Why not just throttle a valve instead of slowing the pump?
Throttling a valve reduces flow by adding resistance, but the pump still runs at full speed and draws close to full power — the wasted energy just turns into heat and noise across the valve. Slowing the pump with a VFD actually reduces the power the motor draws in the first place.
Does reduced speed affect pump head as much as power?
No. Head falls with the square of speed, not the cube — at 80% speed, head drops to about 64% of full-speed head, a smaller reduction than the 51% power figure. This is why VFDs work well for systems where some head reduction is acceptable, such as many circulation and booster applications.
Is this calculation accurate for any pump?
The affinity laws are a close approximation for centrifugal pumps operating on their original system curve, which covers most water circulation, booster and transfer applications. They become less accurate at very low speeds, near a pump's minimum flow limits, or for positive-displacement pumps, which don't follow the same relationship.
Does this include the cost of installing a VFD?
No. This calculator estimates the ongoing energy and cost savings from running at reduced speed, not the upfront cost of a variable frequency drive or its installation. Compare the annual savings figure against a VFD's installed cost to estimate a payback period.
Sources & references
- Hydraulic Institute. (2013). Pump Life Cycle Costs: A Guide to LCC Analysis for Pumping Systems.
- Hydraulic Institute. HI 9.6.6 — Rotodynamic Pumps for Pump Piping.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)