# VFD Pump and Fan Energy Savings Calculator (Affinity Laws)

> Source: https://netray.co/tools/vfd-pump-affinity-law-energy-savings-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Power at reduced speed by the cube law versus throttled constant speed operation, with annual savings and payback.

## Category

maintenance

## Industry

Manufacturing

## Audience

- Reliability engineer
- Energy manager
- Plant engineer

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Input power at full flow

**Key:** full_kw

**Type:** number

**Default:** 30

**Min:** 0.1

**Step:** 0.5

**Unit:** kW

**Help:** Electrical power at 100% speed and design flow.

#### Average operating speed with VFD

**Key:** speed_pct

**Type:** slider

**Default:** 80

**Min:** 40

**Max:** 100

**Step:** 1

**Unit:** %

#### Power at constant speed with throttling

**Key:** throttle_pct

**Type:** slider

**Default:** 90

**Min:** 50

**Max:** 100

**Step:** 1

**Unit:** % of full

**Help:** A throttled pump uses somewhat less than full power at reduced flow. 85 to 95 is typical for centrifugal pumps.

#### Drive efficiency

**Key:** drive_eff

**Type:** number

**Default:** 97

**Min:** 90

**Max:** 99.5

**Step:** 0.5

**Unit:** %

#### Run hours per year

**Key:** hours

**Type:** number

**Default:** 6000

**Min:** 100

**Max:** 8760

**Step:** 100

**Unit:** h

#### Electricity price

**Key:** tariff

**Type:** number

**Default:** 0.12

**Min:** 0

**Step:** 0.01

**Unit:** per kWh

#### Installed VFD cost

**Key:** vfd_cost

**Type:** number

**Default:** 9000

**Min:** 0

**Step:** 500

**Outputs:**

#### Average power, throttled constant speed

**Key:** base_kw

**Expr:** full_kw * throttle_pct / 100

**Format:** decimal

**Description:** kW.

#### Average power, with VFD

**Key:** vfd_kw

**Expr:** full_kw * pow(speed_pct / 100, 3) / (drive_eff / 100)

**Format:** decimal

**Description:** kW, from the cube law including drive losses.

#### Power saved

**Key:** saved_kw

**Expr:** max(0, base_kw - vfd_kw)

**Format:** decimal

#### Energy saved per year

**Key:** kwh_saved

**Expr:** saved_kw * hours

**Format:** integer

**Primary:** true

**Description:** kWh.

#### Cost saved per year

**Key:** cost_saved

**Expr:** kwh_saved * tariff

**Format:** currency

**Primary:** true

#### Simple payback

**Key:** payback_m

**Expr:** if(gt(cost_saved, 0), vfd_cost / cost_saved * 12, 0)

**Format:** months

**Chart:**

#### Average power (kW) vs operating speed

**Type:** line

**X:** speed_pct

**From:** 40

**To:** 100

**Steps:** 30

**Series:**

- vfd_kw
- base_kw

**Disclaimer:** The cube law holds when there is little static head. Systems with high static head save less. A measured system curve is needed for a firm business case.

## Content

**Intro:** For centrifugal pumps and fans, flow varies with speed, head with speed squared and power with speed cubed. A modest speed reduction therefore gives a large power reduction. This calculator estimates the saving against throttling and the payback of a drive.

**Sections:**

#### How to use it

**Body:** Enter the electrical power at full flow, the average speed you expect the drive to run at and how much power the pump draws today when throttled. Add the drive efficiency, run hours, tariff and installed cost. The result is average power, energy and cost savings per year and simple payback. The chart compares the two power curves across speed so you can see where the drive pays off.

#### The affinity laws

**Body:** The affinity laws state that Q2/Q1 = N2/N1, H2/H1 = (N2/N1) squared and P2/P1 = (N2/N1) cubed. Running at 80% speed needs only about 51% of the power, before drive losses. The model divides by drive efficiency to account for losses in the converter. Throttled constant speed does not follow the cube law, so the baseline is an input rather than a formula.

**Bullets:**

- A 10% speed reduction gives roughly a 27% power reduction
- Savings shrink if the system has high static head
- Fixed-flow processes gain nothing from a drive

#### Common mistakes

**Body:** Applying the cube law to positive displacement pumps, which behave nearly linearly, is a frequent mistake. Others are using nameplate rather than measured power, assuming the pump will run at an average speed it never actually reaches, and ignoring minimum speed limits for cooling and bearing lubrication. Log actual flow demand for a few weeks before sizing the business case.

**Bullets:**

- Using nameplate kW instead of measured kW
- Applying fan or pump laws to constant-torque loads
- Ignoring harmonics and cable length for drives

**Cta:** Netray can pull equipment run hours and energy meter data from ERP and historian sources to build a ranked list of drive candidates.

**Faq:**

#### How much does a VFD save on a pump?

**Answer:** It depends on how much flow reduction you need and how much static head the system has. For variable-flow centrifugal pumps with low static head, savings of 20 to 50 percent of energy are commonly seen, but verify with measurements.

#### What is the cube law?

**Answer:** Power required by a centrifugal pump or fan varies with the cube of speed, so a reduction to 80% speed needs about 51% of full power in an ideal case.

#### Does it work for any pump?

**Answer:** No. The laws apply to centrifugal machines. Positive displacement pumps deliver flow proportional to speed and need near-linear power, so savings are much smaller.

#### What payback is reasonable?

**Answer:** Drives on large, long-running, variable-flow loads often pay back in under two years. Short run hours or constant-flow duties can push payback beyond acceptable limits.

## Search terms

VFD energy savings calculator, pump affinity laws calculator, fan law cube power speed, variable speed drive payback, VFD payback calculator, pump speed reduction energy saving, affinity laws power vs speed, VSD savings pump

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