Fan Curve Operating Point Calculator
Find where a fan curve meets a quadratic system curve.
Enter your values
Enter the fan curve shutoff pressure (a) in in wc.
Enter the fan curve coefficient (b) in in wc per CFM^2.
Enter the system curve coefficient (k) in in wc per CFM^2.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Operating airflow
- 200 CFM
- Operating pressure
- 2.4 in wc
- Fan curve check
- 2.4 in wc
Quick answer
The fan operates where the fan's pressure-flow curve intersects the system's resistance curve.
Fan: P = a - b*Q^2; System: P = k*Q^2; solve a - b*Q^2 = k*Q^2
At a glance
| What it does | Find where a fan curve meets a quadratic system curve. |
|---|---|
| Category | HVAC & Airflow |
| Inputs needed | Fan curve shutoff pressure (a), Fan curve coefficient (b), System curve coefficient (k) |
| Main output | Operating airflow |
| Formula | Fan: P = a - b*Q^2; System: P = k*Q^2; solve a - b*Q^2 = k*Q^2 |
| Cost | Free — no sign-up, no download |
How to use the Fan Curve Operating Point Calculator
- 1Fit the fan curve to P = a - b*Q^2 using two points from the manufacturer's curve.
- 2Fit the system curve to P = k*Q^2 using a known design point.
- 3The tool solves the intersection to give the true operating CFM and pressure.
Inputs explained
- Fan curve shutoff pressure (a)(in wc)
- Enter the fan curve shutoff pressure (a) in in wc.
- Fan curve coefficient (b)(in wc per CFM^2)
- Enter the fan curve coefficient (b) in in wc per CFM^2.
- System curve coefficient (k)(in wc per CFM^2)
- Enter the system curve coefficient (k) in in wc per CFM^2.
Worked example
Using the values the calculator loads with:
Inputs
- Fan curve shutoff pressure (a)4.0 in wc
- Fan curve coefficient (b)0.00004 in wc per CFM^2
- System curve coefficient (k)0.00006 in wc per CFM^2
Results
- Operating airflow200 CFM
- Operating pressure2.4 in wc
- Fan curve check2.4 in wc
Frequently asked questions
Where do I get k?
Use a known operating point (design CFM and pressure) and solve k = P / Q^2, or use the system curve calculator.
Why isn't my fan hitting design CFM?
If the actual system resistance (k) is higher than designed, the true operating point shifts to lower flow — common with dirty filters or extra fittings.
What do I need to enter into the Fan Curve Operating Point Calculator?
Just 3 values: fan curve shutoff pressure (a), fan curve coefficient (b), system curve coefficient (k). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Fan Curve Operating Point Calculator work out the answer?
The fan operates where the fan's pressure-flow curve intersects the system's resistance curve. It applies the formula Fan: P = a - b*Q^2; System: P = k*Q^2; solve a - b*Q^2 = k*Q^2 and shows the working so you can check each step by hand.
Is the Fan Curve Operating Point Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.