Fuel Injector Calculator

How fuel injector sizing works

A fuel injector is a valve that is either fully open or shut. While it is open it passes a fixed amount of fuel per minute for a given pressure, its static flow, and the engine’s computer meters fuel by changing how long it stays open on every engine cycle. The share of the cycle it is open is the duty cycle. At full power the injectors have to supply every pound of fuel the engine burns, so sizing comes down to two questions: how much fuel per hour does the engine need, and how much can each injector supply without staying open too long?

The fuel the engine needs comes from its brake specific fuel consumption (BSFC): pounds of fuel burned per horsepower per hour, measured at the crank. A naturally aspirated gasoline engine at full load typically uses 0.45 to 0.50 lb/hp·hr. Turbocharged and supercharged engines are run richer to control detonation and exhaust temperature, usually with less ignition advance, and a supercharger also takes power to drive, so they typically use 0.55 to 0.75. The calculator defaults to 0.65 for them, the figure a fuel-system maker uses in its own boosted examples: when sizing injectors it is better to assume a little too much fuel than too little. Horsepower × BSFC is the total fuel flow in lb/hr, the same figure a bsfc calculator gives you; split it among the injectors and divide by the duty cycle you allow, and you have the injector size.

Everything here applies to port fuel injection, where each injector sprays into its intake port from a rail at a few bar and the engine computer controls only how long it stays open. Direct injection, which sprays into the cylinder from a rail fed by an engine-driven high-pressure pump, works at far higher pressures, and its injectors are specified and calibrated differently, so neither the duty-cycle limits nor the static-flow ratings on this page carry over to a direct-injected engine. Size those systems from the data of the injectors and high-pressure pump themselves.

The duty cycle is kept well short of wide open. Engine management makers put the ceiling at about 85%: beyond that the injector barely closes before the next pulse, and at high rpm its own opening time eats a growing share of the cycle. Designing for 80% leaves room for that, for voltage and pressure variation, and for a little more power later.

What to enter and where to find it

• Crank horsepower. The power you expect at the flywheel. BSFC is defined at the crank, so a chassis dyno figure needs converting with the whp to hp calculator first. Estimate on the high side: an injector that is slightly big is easier to live with than one that runs out.
• Aspiration and fuel. Together they set the typical BSFC when you leave that box empty. The E85 option assumes the highest ethanol content sold as E85, 83%, because it needs the most fuel; the e85 calculator works out what a given blend contains.
• BSFC. Leave it blank for the typical figure, or enter a value from dyno data or your engine builder. It is read as the BSFC on the fuel you chose, so an E85 figure goes in as it is.
• Number of injectors. Normally one per cylinder. Engines with two injectors per cylinder count all of them, as long as they all flow at full power.
• Maximum duty cycle. The share of the time each injector may stay open at peak power. 80% is a common design point; going past 85% is asking for trouble.
• Injector flow and fuel pressure. A flow figure always comes with the pressure it was measured at, commonly 43.5 psi (3 bar), but some data sheets quote a lower or higher pressure, so check it. If your system holds a different pressure across the injector, convert the rating on the Fuel pressure tab before using it on the Duty cycle tab.

The fuel injector size formula

Six relationships, in the units injector data sheets use. The arithmetic is exact for the numbers you enter; the uncertainty sits in the BSFC, which is an estimate unless it comes from a dyno.

1. Total fuel flow (lb/hr) = crank hp × BSFC
2. Injector size (lb/hr each) = crank hp × BSFC ÷ (number of injectors × maximum duty cycle)
3. Duty cycle = crank hp × BSFC ÷ (number of injectors × injector flow)
4. Flow at new pressure = rated flow × √(new pressure ÷ rated pressure)
5. cc/min = lb/hr × 453.59 ÷ 60 ÷ fuel density (g/cc)
6. Catalog rating (n-heptane cc/min) = cc/min of fuel × √(fuel density ÷ 0.684)

The first three are the same equation solved for different unknowns, so the Duty cycle tab is simply the injector size calculator run backward. The fourth is the orifice law, which turns the Fuel pressure tab into an injector flow calculator: flow through a fixed nozzle grows with the square root of the pressure difference across it, so doubling the pressure adds only about 41% more flow. The pressure that counts is the difference between the fuel rail and the intake manifold. A boost-referenced regulator that raises fuel pressure one psi for every psi of boost keeps that difference at the base pressure; a regulator that is not referenced to boost loses one psi of difference for every psi of boost. Every injector also has a maximum operating pressure on its data sheet, and its opening delay grows with pressure, so the square-root figure is a best case at high pressure.

The last formula converts weight to volume. With gasoline at 0.74 kg/L one lb/hr equals 10.22 cc/min; many catalogs use a round factor of about 10.5, which comes from the old rule that gasoline weighs about 6.0 lb/gal (0.72 kg/L). Data sheets are also measured with a test fluid such as n-heptane (about 0.68 kg/L) rather than pump fuel, so lb/hr to cc/min conversions from different sources can disagree by up to about 8%. Compare injectors in the unit their own data sheets use.

The test fluid also changes the flow itself, not just the conversion. Through the same nozzle at the same pressure, the volume of liquid that passes scales with √(test-fluid density ÷ fuel density), so a fuel denser than the test fluid passes a little less volume. The last formula turns the cc/min of your fuel into the rating to look for in a data sheet measured with n-heptane at 0.684 kg/L: 4.0% more for gasoline at 0.74 kg/L, 6.8% more for E85 at 83% ethanol and 7.5% more for methanol. The calculator shows it as Catalog rating needed. If a data sheet names a different test fluid, or gives the flow for gasoline, use its own figure instead.

Fuel injector size for E85 and methanol

Alcohol fuels carry oxygen in the molecule, so each pound needs less air to burn completely: 9.0 lb of air for ethanol and 6.47 lb for methanol, against 14.7 lb for gasoline. The energy released per pound of air is almost the same for all three, so an engine making the same power takes in about the same air and needs proportionally more fuel. That is the basis of this fuel injector size calculator for E85: fuel needed = gasoline fuel × gasoline’s stoichiometric ratio ÷ the fuel’s stoichiometric ratio, at the same lambda.

Fuel sold as E85 contains anywhere from 51% to 83% ethanol depending on season and region. At the top of that range its stoichiometric ratio is 9.92, so it takes 48% more fuel by weight than gasoline, or about 40% more by volume because it is denser. At the bottom of the range the extra is 26%. The calculator sizes for the top of the range, so the injectors still keep up with the richest blend at the pump. Methanol needs 2.27 times the weight of fuel gasoline does at the same lambda.

A fuel-system maker publishes observed BSFC ranges for alcohol engines, shown in the table below. The stoichiometric estimate lands at or a few percent above the top of those ranges for E85 and for naturally aspirated methanol, which errs toward more fuel. In general the default is the stoichiometric estimate or the published minimum for that fuel, whichever is higher.

Boosted methanol is the exception that needs explaining. The 1.80 to 2.00 lb/hp·hr range comes from a fuel-system maker’s sizing guidance, which presents its BSFC figures as observations from experience, not as a formula. It reflects boosted methanol engines run very rich, with the extra fuel used to cool the charge and the combustion chamber, as alcohol racing engines often are. The calculator uses the bottom of that range, 1.80, because it is the published minimum, but that is still about 22% more than the same-lambda estimate of 1.48. For a street or track turbo engine run nearer the maximum-power mixture, it oversizes the injectors: if yours is calibrated that way, enter a BSFC closer to the estimate, or one from your own dyno data.

One more detail for alcohol fuels. Injector flow ratings are measured with a test fluid, usually n-heptane, that is lighter than gasoline and lighter still than E85 or methanol, and a denser fuel passes a little less volume but a little more weight through the same nozzle. The calculator corrects the cc/min for that: on E85 at 83% ethanol the catalog rating to look for is 6.8% above the cc/min of fuel, and on methanol 7.5% above. A lb/hr rating worked out from the test fluid’s weight sits below the weight of alcohol the injector passes by the same factor, so comparing the lb/hr result with such a rating slightly understates what the injector can deliver.

Injector duty cycle and pulse width

Used as an injector duty cycle calculator, the second tab takes the flow of the injectors you have and shows the share of the time they must stay open at your power, plus the power they support at the duty limit you choose. If the result is more than the whole cycle, the engine needs more fuel than the injectors can deliver even held wide open.

Datalogs usually show pulse width in milliseconds instead of duty cycle. A four-stroke engine injects once per cycle and a cycle takes two crank revolutions, so it lasts 120,000 ÷ rpm milliseconds, and duty cycle (%) = pulse width (ms) × rpm ÷ 1,200. At 6,000 rpm a cycle lasts 20 ms, so a 16 ms pulse is already 80% duty. Part of every pulse is the injector’s opening delay, during which almost no fuel flows, which is one more reason the usable limit stops well short of wide open.

Worked example

Four typical questions, worked out with the same functions that run the calculator.

Typical BSFC by fuel and aspiration

BSFC depends on the engine, the power adder and how rich it is run, so treat these as starting points rather than facts about your engine. The published ranges for gasoline come from injector sizing practice, and the ranges for ethanol fuels (the maker’s figures match E85-type blends) and methanol from a fuel-system maker’s guidance. For gasoline the calculator’s default is the top of the naturally aspirated range and, for boosted engines, the figure that maker uses in its own examples; for E85 and methanol it is the gasoline figure scaled by stoichiometry, or the published minimum where that is higher, as explained above.

Aspiration matters as much as fuel: a boosted engine burns noticeably more fuel per horsepower than a naturally aspirated one on the same fuel, so a turbo build needs bigger injectors than a naturally aspirated engine of the same power. The fuel column is also the starting point for the fuel pump calculator, which turns it into the pump flow you need.

Common mistakes

• Using wheel horsepower. BSFC is per crank horsepower. A chassis dyno figure undersizes the injectors by the whole drivetrain loss.
• Sizing for wide-open injectors. An injector held open all the time has no control left and its flow cannot rise any further. Size for 80% and keep the rest as reserve.
• Ignoring the rating pressure. A flow figure means nothing without its pressure, and it does not scale in proportion: in the example, 33% more pressure gave only 15.5% more flow.
• Leaning on pressure to rescue small injectors. Flow grows only with the square root of pressure, and pumps deliver less as pressure rises. Check the pump with the fuel pump calculator before counting on extra pressure.
• Using a gasoline BSFC with E85. Choose E85 in the fuel box or enter an E85 figure. A gasoline BSFC applied to E85 at the top of its range leaves the injectors about 33% too small.
• Using it for direct injection. The duty-cycle limits and static-flow ratings here are those of port injection. A direct-injected engine needs the data of its own injectors and high-pressure pump.
• Mixing conversion factors. The cc/min per lb/hr factor depends on the density assumed, and so does the test fluid, so two catalogs can list the same injector with numbers up to about 8% apart. Compare like with like.