Pump and Fan Affinity Laws Calculator
Flow, head and power at a new speed, with the power saved and what that saves in a year.
Results
What this tool does
Flow follows speed directly, head follows its square and power follows its cube — which is why throttling a valve to reduce flow is so wasteful compared with slowing the machine down. The same three laws apply to fans, and they are the entire economic case for variable speed drives in buildings and in process plant.
Formula
Q ∝ N ; H ∝ N² ; P ∝ N³
Variables
| Symbol | Meaning | Unit |
|---|---|---|
q1 | Flow rate | m³/h |
h1 | Head | m |
p1 | Power | kW |
n1 | Rotational speed | rpm |
n2 | Rotational speed | rpm |
Q2 | Flow rate | m³/h |
H2 | Head | m |
P2 | Power | kW |
SV | Percentage | % |
EY | Energy | kWh/a |
Worked example
- Flow rate50 m³/h
- Head30 m
- Power6.5 kW
- Rotational speed2900 rpm
- Rotational speed2320 rpm
- Flow rate40.000 m³/h
- Head19.200 m
- Power3.3280 kW
- Percentage48.80 %
- Energy27,787 kWh/a
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
Frequently asked questions
Does a speed drive really save that much?
The cube law is real and it is why variable speed drives pay for themselves on pumps and fans: twenty percent less speed is very nearly half the power. But the laws assume the system curve passes through the origin, which is true for friction-dominated circuits and false wherever there is a static lift or a fixed pressure to overcome. With a large static head the savings are far smaller, and the pump can drop off its curve entirely at low speed.