Estimate annual pumping energy and cost, then compare a VFD against a throttled valve — modelled on the real system curve, so static head is handled honestly instead of just cubing the flow.
US + metric
Formula shown
Shareable results
Pump Energy Cost & VFD Savings
hp
%
h
d
VFD vs throttled valve (system-curve model)
ft
ft
%
%
$
Annual energy (design point)
46,700 kWh
Annual cost
$5,600
Cost per unit volume
$0.052 per 1,000 gal
VFD annual saving$1,490/yr(payback 5.37 yr)
Throttled valve (annual)
$4,590/yr
VFD (annual)
$3,100/yr
10-year saving
$14,900
At 40% static head, the VFD saves $1,490/yr. With no static head (pure cube law) it would show $2,140/yr — cubing the flow ratio overstates the saving.
Power vs flow: the gap between the throttle line and the VFD (system-curve) line is the energy the VFD saves. Higher static head lifts the VFD line and shrinks the gap.
Formula & method
VFD: P(f) = P · f·(Hstatic + Hfriction·f²) / Hdesign ÷ ηvfd · Throttle: P(f) = P · (a + (1−a)·f)
The VFD model follows the system curve, so it captures static head — cubing the flow ratio is only valid at zero static head. The throttle model uses a power-floor approximation (default 40% of full power near zero flow). Simple payback ignores discounting and escalation.
For preliminary analysis and educational use. Verify against measured power, motor and drive data, and applicable codes; final designs should be reviewed by a licensed professional engineer.
Pumping energy cost is simply electrical power times hours times the electricity rate — but the interesting question is how much a variable-frequency drive would save versus throttling a valve. This calculator estimates the annual energy and cost at your operating point, then compares a VFD against a throttled valve across your load profile, modelling the real system curve rather than blindly cubing the flow ratio.
Worked example
A 16 hp pump on a 92%-efficient motor draws about 13 kW. Running 12 hours a day, 300 days a year, at $0.12/kWh, that is roughly 46,700 kWh and $5,600 a year. Over a varying load profile with 40% static head, a VFD cuts the annual bill from about $4,600 (throttled) to about $3,100 — a saving near $1,500 a year, paying back an $8,000 drive in about 5.4 years.
Why cubing the flow ratio is usually wrong
The affinity laws say power falls with the cube of speed — so it is tempting to claim a VFD at 50% flow uses only 12.5% of the power. That is only true when the system has zero static head. Real systems lift fluid to a height or into a pressurised vessel, and that static head does not fall with flow. On the system curve, the head the pump must produce stays near the static head as flow drops, so power falls far less steeply than the cube law predicts. The higher the static-head fraction, the smaller the VFD saving. This tool shows that sensitivity explicitly: it reports what the same case would “save” at zero static head, so you can see how much the cube-law shortcut overstates the benefit.
When VFDs pay off
VFDs return the most on systems that are friction-dominated (low static head) and that spend significant time at reduced flow. On a high-static-head system that runs mostly at full flow, a VFD may barely pay back — and it even adds a few percent of drive losses at full speed. Enter your real load profile and static-head split to get an honest number, and compare the lifetime picture with the life cycle cost calculator.
Variables
Symbol
Meaning
US unit
SI unit
P_elec
Electrical input power at the design point
kW
kW
f
Flow as a fraction of design flow
-
-
H_stat
Static head
ft
m
H_fric
Friction head at design flow
ft
m
u03b7_vfd
VFD (drive) efficiency
-
-
a
Throttle power floor (fraction of full power near zero flow)
