Automotive, Diesel & Motorsports Cylinder Heads, Camshafts & Airflow Orifice flow scaling (√Δp) with the 0.257 hp/CFM correlation

Cylinder Head Airflow Horsepower Potential Calculator

A flow bench gives you cubic feet per minute at one test depression. Two numbers you actually want are not on the sheet: what that flow is worth in horsepower, and what the same port would read on a bench set to a different depression. This calculator does both. Enter the measured CFM and the depression it was taken at, and you get the flow normalised to the 28 in-H₂O industry reference, the peak horsepower that flow can support across your cylinder count, the same flow restated at any other depression, and the CFM a target power figure demands.

Calculator

This calculator runs in your browser. Enable JavaScript for live results — the inputs, formula and worked example below remain fully readable without it.

Inputs this calculator takes, with typical values
InputWhat to enterExample
Measured intake port flowPeak intake flow for one port, at whatever depression your bench was set to.250 CFM
Test depression usedThe pressure drop your bench held across the port, printed at the top of every flow sheet.28 in-H2O
Depression to convert toThe depression you want the same port's flow restated at, for comparing sheets from different shops.10 in-H2O
Number of cylindersEach cylinder is fed by one intake port, so this scales single-port flow to the whole engine.8
Horsepower per CFM at 28 in-H2OEmpirical coefficient linking port flow to peak power; 0.257 is the widely used figure for a well-matched naturally aspirated combination.0.257
Target horsepowerThe power figure you want, used to work backwards to the flow each port must supply.500 hp

It returns

  • Peak horsepower potential — What this much intake flow can support in a well-matched naturally aspirated engine.
  • Flow normalised to 28 in-H2O
  • Flow at the target depression
  • Horsepower per cylinder
  • Flow per port needed for the target
  • Flow surplus over the target

The formula

CFM2=CFM1Δp2Δp1
CFMreq=HPtargetkN

In plain text: CFM₂ = CFM₁·√(Δp₂/Δp₁); HP ≈ CFM₂₈ · k · N

  • CFM₁Flow measured at the bench's test depression (cu ft/min)
  • Δp₁Depression the measurement was taken at (in-H₂O)
  • Δp₂Depression you want the flow restated at (in-H₂O)
  • CFM₂₈Flow normalised to the 28 in-H₂O reference (cu ft/min)
  • kHorsepower per CFM at 28 in-H₂O (hp/CFM)
  • NNumber of cylinders (count)

The square-root scaling is the incompressible orifice relation and holds well at bench depressions, where the pressure drop is around 1 psi. The horsepower coefficient is an empirical correlation, not a law.

Updated Category Cylinder Heads, Camshafts & Airflow Verified against published test cases Reading time 10 min

What a flow number means and what it does not

A flow bench holds a fixed pressure difference across a port and measures the air that passes. The result — cubic feet per minute at a stated depression and a stated valve lift — is a measure of the port's resistance, not of the engine's output. It becomes a horsepower figure only through an empirical correlation, and only for an engine whose cam, induction, exhaust and displacement can actually use the flow.

Two things stop raw flow numbers from being comparable between shops. The first is the test depression. A bench set to 10 in-H₂O reads far lower than the same port on a bench set to 28 in-H₂O, and the ratio is not linear. The second is valve lift: a sheet is a curve, and quoting the peak number without the lift it occurred at hides whether the engine's camshaft ever reaches that lift. This calculator solves the first problem exactly and gives you the tools to reason about the second.

Use it to compare castings honestly, to sanity-check a supplier's claim, and to decide whether the head is the limit in a build before you spend money porting one that already flows more than the target needs.

Why flow scales with the square root of depression

Air passing through a restriction behaves like flow through an orifice. For an incompressible fluid, Bernoulli's relation gives a velocity proportional to the square root of the pressure drop, and since volumetric flow is velocity times area, the flow through a fixed port follows the same rule:

CFM₂ = CFM₁ × √(Δp₂ / Δp₁)

That is the whole conversion. Going from 28 in-H₂O down to 10 in-H₂O multiplies the reading by √(10/28) = 0.5976, so a 250 CFM port reads 149.4 CFM. Going the other way multiplies by √(28/10) = 1.6733. Notice the consequence: quadrupling the test depression only doubles the reading, which is why a shop quoting big numbers at 28 in and a shop quoting modest numbers at 10 in may be measuring identical castings.

The incompressible assumption is reasonable here. 28 in-H₂O is about 1.01 psi, roughly 7% of atmospheric pressure, so density changes across the port are small and the square-root law holds closely. It degrades at very high depressions and where a port chokes, which is one reason benches settled on a common reference in the first place.

The horsepower step is different in kind. It is a correlation drawn from dynamometer results, popularised by David Vizard, that a well-matched naturally aspirated engine makes roughly 0.257 hp for every CFM of intake flow at 28 in-H₂O, per cylinder. Equivalently, each horsepower needs about 3.9 CFM of intake port flow at that depression. It is an upper bound on what the head permits, not a promise about what the engine will make.

Worked example: a 250 CFM head on a V8, and a sheet from another shop

You have a flow sheet showing 250 CFM at 0.600 in lift, taken at 28 in-H₂O, for a V8.

  1. Already at the reference. The scale factor is √(28/28) = 1, so CFM at 28 in-H₂O is 250.0.
  2. Horsepower per cylinder. 250 × 0.257 = 64.25 hp.
  3. Whole engine. 64.25 × 8 = 514 hp of potential.
  4. Restated at 10 in-H₂O. 250 × √(10/28) = 250 × 0.597614 = 149.4 CFM.

Now a competing shop quotes a head at 160 CFM, tested at 10 in-H₂O. Is it better or worse?

  1. Normalise it. 160 × √(28/10) = 160 × 1.673320 = 267.7 CFM at 28 in-H₂O.
  2. Its potential. 267.7 × 0.257 × 8 = 550 hp.

The head that looked like it flowed 160 against your 250 in fact flows 7.1% more — 267.7 ÷ 250 − 1 = 7.1% — and supports about 36 hp more. Comparing the raw figures would have led you to the wrong casting.

Finally, work backwards from a target. For 500 hp on eight cylinders at 0.257: 500 ÷ (0.257 × 8) = 500 ÷ 2.056 = 243.2 CFM per port. Your 250 CFM head has 6.8 CFM in hand, so the head is not what stands between the engine and 500 hp.

How to read the horsepower potential figure

Treat it as a ceiling the cylinder head imposes, not a prediction. Reaching it requires everything else to be matched: a camshaft with enough duration and lift to use the port, an intake manifold and throttle that do not become the new restriction, an exhaust that lets the cylinder blow down, and enough displacement and rpm to move that much air in the first place.

The correlation also assumes the flow figure is one the engine can reach. A sheet peaking at 0.700 in lift is irrelevant to a cam that only opens the valve 0.520 in. Read the flow at your actual net valve lift — work that out with the rocker arm ratio and valve lift calculator if you are changing rockers — and use the flow at that lift, not the peak on the sheet.

When the calculated potential comes out well above what the engine makes on the dyno, the head is not the limit and porting it further will not help. Look at cam timing, intake runner length, exhaust and the induction system instead. When it comes out below the dyno figure, either the sheet is optimistic, the coefficient is being applied to a lift the engine does not reach, or the engine is not naturally aspirated — boosted engines break this correlation entirely, because the compressor supplies pressure the port never had to earn.

Airflow demand also has a cross-check from the other direction. Work out the mass flow the engine needs at your target rpm with the compressor airflow calculator or the induction demand with the carburettor CFM calculator, and see whether the head's ceiling and the engine's demand land in the same place.

Horsepower potential from intake port flow at 28 in-H₂O

Each cell is flow per port × 0.257 × cylinder count. Read the row for your head's flow at the lift your camshaft actually reaches.
CFM per port at 28 in-H₂Ohp per cylinder4 cylinders6 cylinders8 cylinders
20051.4206308411
22557.8231347463
25064.3257386514
27570.7283424565
30077.1308463617
35090.0360540720
400102.8411617822

Rounded to the nearest horsepower. The figures are a ceiling set by the cylinder head, achievable only when cam, induction, exhaust and displacement are matched to it.

Depression conversion factors from 28 in-H₂O

Multiply a flow figure taken at 28 in-H₂O by the factor to restate it at another depression; divide to go the other way.
Target depression (in-H₂O)Factor from 28 in250 CFM becomes
100.5976149.4
150.7319183.0
200.8452211.3
250.9449236.2
281.0000250.0
351.1180279.5

Each factor is the square root of the depression ratio: √(10/28) = 0.5976, √(35/28) = 1.1180.

Mistakes that make a flow comparison worthless

  • Comparing depressions without converting. The most common error on forums, and it is worth 67% between a 10 in and a 28 in sheet on the same port.
  • Quoting peak flow instead of flow at your lift. A number recorded at 0.700 in lift is meaningless for a cam that opens the valve 0.520 in. Use the row of the sheet that matches your net lift.
  • Ignoring exhaust flow. The intake port sets the ceiling, but a poor exhaust-to-intake ratio limits what the engine can reach in practice. Most builders want the exhaust port flowing somewhere around 70 to 80% of the intake, and a head far below that will not deliver its intake-side potential.
  • Applying the correlation to a boosted engine. The 0.257 figure comes from naturally aspirated dynamometer results. A compressor supplies the pressure ratio the port would otherwise have to earn, so a boosted engine routinely exceeds the ceiling this page calculates.
  • Forgetting that flow is per port, not per engine. Enter the flow for one intake port and let the cylinder count do the multiplication. A total-engine flow figure divided incorrectly is a factor-of-eight error.

Where head flow sits among the other limits

A naturally aspirated engine's power is set by how much air it can pass per unit time, and the cylinder head is only one of four things standing in the way. The other three are induction (throttle, manifold and, on a carburetted engine, venturi area), camshaft timing, and the exhaust's ability to empty the cylinder before the intake opens.

Work in that order. Size the head's flow ceiling here, then check whether the cam has the duration and lift to reach it — the camshaft duration and overlap calculator converts a cam card into the actual valve events — and finally confirm the induction can pass the same mass of air. Any one of the four can cap the engine, and spending on the other three while one remains the limit buys nothing.

If you are pricing a porting job, the calculation to make first is the one at the end of the worked example: divide your target power by the coefficient and the cylinder count to get the CFM each port must supply, and compare that with what the casting already flows at your valve lift. Heads with 20 CFM in hand do not need porting; heads 40 CFM short may not get there at all without a different casting.

Frequently asked questions

How do I convert flow from 10 inches to 28 inches of water?

Multiply by the square root of the depression ratio: √(28 ÷ 10) = 1.6733. A port reading 160 CFM at 10 in-H₂O is flowing 267.7 CFM at 28 in-H₂O. Going the other way you multiply by √(10 ÷ 28) = 0.5976. The relation holds because flow through a fixed restriction is proportional to the square root of the pressure drop across it.

How much CFM do I need per horsepower?

About 3.9 CFM of intake port flow at 28 in-H₂O per horsepower, which is the reciprocal of the 0.257 hp/CFM coefficient this calculator uses by default. In practical terms a 500 hp naturally aspirated V8 needs each of its eight intake ports flowing roughly 243 CFM at 28 in-H₂O, at the valve lift the camshaft actually reaches.

Where does the 0.257 hp per CFM figure come from?

It is an empirical correlation drawn from dynamometer testing and popularised by David Vizard in his cylinder-head and porting work. It is not derived from thermodynamics and it is not a standard: it summarises what well-matched naturally aspirated engines have been observed to make from a given intake port flow. The input field lets you change it if your own dyno data supports a different figure for the kind of engine you build.

Does the horsepower potential figure account for the camshaft?

No, and that is the main limitation. The correlation assumes the camshaft, induction and exhaust are matched to the head. A cam that never opens the valve to the lift where the flow was measured cannot use that flow, and a restrictive intake manifold becomes the limit regardless of what the port does on a bench. Read the flow at your actual net valve lift and treat the result as a ceiling.

Why does my engine make less power than the calculated potential?

Because the head is not the limiting component in your combination. The most frequent causes are a camshaft with too little duration or lift to reach the flow, an intake manifold or throttle body that restricts before the port does, an exhaust that cannot blow the cylinder down, or a displacement and rpm combination that simply does not demand that much air. The figure this page gives is what the head permits, not what the engine will produce.

Should I use intake or exhaust flow in this calculator?

Intake. The correlation is built on intake port flow, so entering an exhaust figure will give a badly inflated result. Exhaust flow matters as a ratio: builders generally want the exhaust port flowing somewhere in the region of 70 to 80% of the intake at the same lift, and a head far below that band will not deliver the intake-side potential no matter how well the intake flows.

Does this work for turbocharged or supercharged engines?

The depression conversion works for any port on any engine, because it is fluid mechanics. The horsepower correlation does not: it was drawn from naturally aspirated results, and a boosted engine pushes air through the port at a pressure ratio the port never had to generate itself, so it routinely exceeds the ceiling this page calculates. For boosted work, size the airflow from displacement, rpm, volumetric efficiency and manifold pressure instead.

What test depression should I ask a shop to use?

28 in-H₂O, because it is the de facto industry reference and makes sheets directly comparable. Some shops use 25 in-H₂O and older data is often at 10 in-H₂O; both are perfectly valid measurements and convert exactly with the square-root relation. What matters far more than the depression is that the sheet lists flow at every lift step rather than a single peak number.

References

  • Internal Combustion Engine Fundamentals, 2nd ed. (flow through restrictions, volumetric efficiency) — McGraw-Hill Education (John B. Heywood)
  • How to Port and Flow Test Cylinder Heads — HP Books (David Vizard)
  • Design and Simulation of Four-Stroke Engines — SAE International (Gordon P. Blair)