What is average effective braking pressure?

The BMEP is the average pressure acting on the piston and producing the torque that is actually measured by a dynamometer. It is not a measurable pressure but rather a number to standardize comparisons. It is valuable because it allows engines of different sizes to be compared on the same scale.

What is the formula for BMEP?

BMEP = 2 x π x n x T / D, where T is the brake torque, D is total displacement and n is crankshaft revolutions per expansion stroke. For four-stroke engines this is 2, for two-stroke engines it's 1. In yard-pound units the same relationship can be simplified to: BMEP (psi) = 150.8 x Torque in pound feet / Displacement in cubic inches, for four-stroke engines.

What are good values for brake mean effective pressure (BMEP)?

Most modern unboosted road-going gasoline engines have a BMEP of about 11 to 13 bar (about 160 to 190 psi). High performance street engines can reach up to 14 bar, while race engines such as those in Formula One or NASCAR often see values from 15 to 16 bar. Values above about 17 bar usually indicate a turbocharged engine, diesel engine, or an engine with fuel that contains its own oxygen.

Why doesn't the BMEP depend on engine speed?

The speed is balanced in the calculation process. The power is the product of torque and speed, and work per cycle results from dividing the power by the ignition frequency. Ignition frequency is also proportional to the speed. As the remaining value represents the work per cycle and cylinder content, data at 2000 rpm can be directly compared with data at 7000 rpm, provided that the torque was correctly measured.

Can we compare engines with turbochargers to aspirated engines?

A direct comparison is not possible. Supercharged engines pump more air into the cylinder due to their higher volume of air, so BMEP generally increases proportionally with the boost pressure ratio. When the supercharger function is enabled, the calculation tool divides the BMEP by this pressure ratio to bring the engine onto a scale that is closer to a naturally aspirated engine. This is not an exact correction but a plausibility check.

What is the difference between BMEP, IMEP and FMEP?

IMEP is derived from the pressure-time curve in the cylinder and represents work done by combustion. BMEP is derived from torque at the crankshaft and represents power output. The difference between these two values is FMEP. This corresponds to the pressure representing all losses of work due to friction, pumping loss, and the force required to drive the engine itself. The quotient of BMEP divided by IMEP gives the mechanical efficiency.

Does a higher BMEP mean a more efficient engine?

It means higher power per displacement but is not the same as thermal efficiency. It's possible to increase the BMEP by boosting or using a richer mixture while consuming more fuel per work done. The BMEP measures the workload on the displacement and not how efficiently the fuel was used.

BMEP Calculator (Brake Mean Effective Pressure)

Engine and dyno figures

Engine cycle

A four-stroke cylinder fires once every two crank revolutions, a two-stroke once every revolution. Pick Custom for an odd-fire, six-stroke or experimental cycle.

Four-stroke (n = 2)

Two-stroke (n = 1)

Custom number of revolutions

Engine displacement (total swept volume)

Brake torque at the crankshaft

Brake mean effective pressure (BMEP)

Enter any two of displacement, torque and BMEP. The calculator solves for the one you leave blank, so it works forwards from a dyno sheet and backwards from a target pressure.

Add the engine speed to get power

Enter the rpm at which that torque was measured and the calculator adds brake power, kilowatts per litre and horsepower per litre.

Compare indicated and brake pressure

Enter the indicated torque from a cylinder-pressure trace to split out IMEP, FMEP, friction torque and mechanical efficiency.

Correct for boost pressure

Divide the BMEP by the manifold pressure ratio to get the naturally aspirated equivalent, so a turbo engine can be judged on the same scale.

Work the displacement out from bore and stroke

Enter the bore, the stroke and the cylinder count and the calculator returns the swept volume per cylinder and for the whole engine.

Please input values into the fields

How your engine compares

Show the comparison charts

Your engine plotted against published BMEP levels, plus what happens to power and BMEP as the crank speed rises.

Show the reference table

The torque your engine would need to reach each published BMEP level.

Two engines produce the same amount of torque. One is a 1.4 liter four-cylinder engine and the other is a 5.7 liter V-8 engine. Which engine has more work to do?

Torque alone cannot answer this question, nor can power. However, the mean effective pressure (MEP) can be used to answer it. This is the work done by the engine divided by the volume of the cylinder that the engine uses to produce that power.

This calculator will give you the BMEP in bar and psi when given the displacement and torque. You can also leave one of the inputs blank to work backwards to find out what torque is required for a certain pressure.

What does the BMEP actually measure?

Imagine an average pressure. If this pressure is pushing the piston evenly from top dead center to bottom dead center, then there will be a torque that could be measured by a dynamometer. This value is the mean effective brake pressure (BMEP).

This is not a pressure that can be measured with a sensor. The actual cylinder pressure exceeds 50 bar briefly at top dead center and then falls rapidly as the piston moves down. BMEP is an equivalent value represented by a horizontal line, it is not a physical measurement but an indicator to calculate energy flows.

The word "brake" indicates the origin of this value, meaning that the torque measured at the crankshaft gauge has already been partially consumed by friction and oil, water, and fuel pumps. Thus BMEP represents work actually produced by the engine rather than work produced by combustion.

Formula for BMEP:

For every piston engine.

\mathrm{BMEP} = \frac{2 \pi \, n \, T}{D}

The three values required are as follows:

Symbol	Meaning	Typical units
T	Brake torque measured at the crankshaft	newton metres, pound-feet
D	Total swept displacement of every cylinder	cubic centimetres, litres, cubic inches
n	Crank revolutions per power stroke	2 for a four-stroke, 1 for a two-stroke

If newton meters and cubic meters are used as units then the result is in pascals. Dividing by 100,000 gives bar, dividing by 6894.76 gives psi. Regardless of which units you use this calculator will perform the appropriate conversion.

Why is n equal to 2 for a four-stroke engine.

A four-stroke engine goes through the intake, compression, power and exhaust strokes before returning to its starting point. The crankshaft must make two full revolutions for this to happen. Therefore, ignition happens every other revolution.

In a two-stroke engine the same cycle is completed in one revolution, which means that the firing frequency is twice as high. If you put the same torque and displacement into the formula, then the BMEP (Mean Effective Pressure) of a two-stroke engine will be half that of a four-stroke engine.

This is not a deficiency of this metric but exactly what it says. A two-stroke engine must produce the same torque as a four-stroke engine even though it has twice as many working cylinders which means that the work done per working cycle must be half as much.

Example calculation:

The Ferrari 458 Italia is equipped with a 4497 cm³ V8 engine that produces a torque of 540 newton meters at 6000 rpm. As it is a four-stroke engine, n = 2.

First, the volume of cubic capacity is converted into cubic meters. 4497 cc corresponds to 0.004497 cubic meters. This results in the following:

\mathrm{BMEP} = \frac{2 \pi \times 2 \times 540\ \mathrm{N \cdot m}}{0.004497\ \mathrm{m^3}} = 1{,}508{,}970\ \mathrm{Pa}

1{,}508{,}970\ \mathrm{Pa} = 15.09\ \mathrm{bar} \qquad = 218.9\ \mathrm{psi}

It is an excellent performance when a petrol engine reaches a value of just over 15 bars. Most road vehicles are in the range of 11 to 13 bars.

A shorthand for the yard-pound units used by all engine manufacturers.

US test bench software almost always uses lbf, cubic inches and psi which simplifies the whole formula down to a single constant.

\mathrm{BMEP\ (psi)} = \frac{150.8 \times T\ \mathrm{(lb\text{-}ft)}}{D\ \mathrm{(cu\ in)}} \qquad \text{four-stroke}

\mathrm{BMEP\ (psi)} = \frac{75.4 \times T\ \mathrm{(lb\text{-}ft)}}{D\ \mathrm{(cu\ in)}} \qquad \text{two-stroke}

Horsepower is the result of torque multiplied by engine speed, divided by 5252. One horsepower equals 33,000 foot-pounds per minute. Combining these relationships gives us 75.39985 by multiplying 12 by 33,000 and dividing by 5252, which is usually rounded to 75.4. For a four-stroke engine, this doubles to 150.8.

Notice what is in these equations: torque divided by displacement volume, and nothing else. Many engine builders leave this constant out entirely and instead show the torque ratio directly, which is stated as pound-feet per cubic inch. This calculator shows both.

What is a good bmev?

The BMEP (mean effective pressure) only has meaning in comparison and this comparison must be fair. A comparison between a turbo diesel and a naturally aspirated petrol engine will provide little meaningful results as the intake air is different.

The data given for maximum torque in specialist literature is as follows:

Engine	BMEP (bar)	BMEP (psi)
Small tuned two-stroke, piston ported	9.9	143
Naturally aspirated aircraft engine, pushrod	11.3	163
Typical modern petrol road car	12 to 13	174 to 189
Strong naturally aspirated road engine	14.2	206
Formula 1 V8 under the 2006 rules	15.2	220
NASCAR Cup V8	15.6	226
Engine Masters winner, naturally aspirated pushrod	16.9	245
Turbocharged road diesel	20.5 and up	297 and up
Top Fuel dragster	about 45	about 650

This trend is worth looking at in detail. The data for all petrol engines are concentrated roughly between 9 and 17 bar, and to achieve this upper value requires extensive development measures. Engines that exceed this range either use supercharging (e.g. turbocharger), compression ignition or a system in which the fuel itself contains oxygen.

This concentrated distribution is the reason why BMEP can act as a "lie detector". If an engine on a test bench shows that it has reached 20 bar with a standard cylinder head then this graph is false. For decades people have used this method to expose exaggerated power claims.

Backward calculation:

If a column is left blank this calculation tool will switch to mode to determine that value.

If you leave the torque blank and enter your target BMEP value, then the calculator will return the torque that should be produced by the engine displacement.

T = \frac{\mathrm{BMEP} \times D}{2 \pi \, n}

If you leave the volume blank, it will return the size of an engine that can produce this torque at a given rpm and a given BMEP.

D = \frac{2 \pi \, n \, T}{\mathrm{BMEP}}

Engine designers often start with the second approach; they pick a realistic BMEP for the type of engine being designed, determine the torque required by the vehicle and then work out the displacement from there.

Add speed

The BMEP does not take into account how fast the crankshaft is rotating, but power is strongly affected by this.

P = \frac{2 \pi \, N \, T}{60} \qquad \mathrm{hp} = \frac{T\ \mathrm{(lb\text{-}ft)} \times \mathrm{rpm}}{5252}

If you activate the 'rpm' option, the calculation tool adds braking power, kilowatts per litre and horsepower per litre to the pressure data.

These two data types answer different questions. The BMEP value tells how much work is done per cycle and per displacement volume. Power per litre gives the amount of work done per second, which means that engines that can spin faster have an advantage. The difference in BMEP between a Formula 1 engine and a NASCAR engine is less than 0.5 bar, but the vastly higher power per litre of the F1 engine is simply because it can run at much higher revs (19,000 rpm).

IMEP, FMEP, mechanical efficiency

There are two other similar metrics like the BMEP and when you combine all three of them together then that's how you can see where the combustion energy has gone.

The indicated mean effective pressure (IMEP) is based on the calculation of torque from the cylinder pressure profile and represents work before losses. The friction mean effective pressure (FMEP), in contrast, represents the fraction of work produced by combustion that is lost before it arrives at the crankshaft end. This includes frictional losses in bearings and piston rings, windage, and the work consumed by oil, water, and fuel pumps.

\mathrm{FMEP} = \mathrm{IMEP} - \mathrm{BMEP} \qquad \eta_m = \frac{\mathrm{BMEP}}{\mathrm{IMEP}}

Let's take a 2.2 liter four cylinder engine as an example. The stated torque is 250 Newton meters, the measured brake torque is 230. With a bore diameter of 85 mm and a stroke of 97 mm, the displacement volume of each cylinder is 550.4 cm³ and the total displacement is 2201.7 cm³.

\mathrm{IMEP} = \frac{2 \pi \times 2 \times 250}{0.0022017} = 14.27\ \mathrm{bar}

\mathrm{BMEP} = \frac{2 \pi \times 2 \times 230}{0.0022017} = 13.13\ \mathrm{bar}

Hence the FMEP is 1.14 bar and the mechanical efficiency is 92 percent. The missing torque of 20 Newton meters is the frictional torque, which corresponds to another representation: a loss of also 8 percent.

Mechanical efficiency is not a fixed quantity. At low load the mechanical efficiency falls as effective work output reduces while friction remains nearly constant. This is also an important reason why fuel consumption appears particularly high at part throttle opening.

The loading pressure changes the scale.

Turbochargers and superchargers allow more air to be forced into an engine of the same displacement, which allows more fuel to be burned and increases BMEP (mean brake effective pressure). However this does not mean that the basic design of the engine needs to be better.

A crude correction method is to divide by the pressure ratio, absolute intake manifold pressure divided by ambient pressure.

\mathrm{BMEP_{corrected}} = \frac{\mathrm{BMEP}}{\left(p_{\mathrm{boost}} + p_{\mathrm{atm}}\right) / p_{\mathrm{atm}}}

If a 2.0 litre engine produces 600 Nm of torque then the uncorrected BMEP is 37.7 bar. This value appears unrealistically high compared to any naturally aspirated engine. At an intake pressure of 1.5 bar, the pressure ratio becomes 2.48 and the corrected figure falls to about 15.2 bar. This is a very good motor and its performance is now expressed in meaningful terms.

This correction should not be considered a physical conclusion but rather an examination of plausibility. It ignores the intake air temperature, the intercooler, the pumping work recovered by the turbocharger and the fact that supercharged engines generally have lower compression ratios.

Calculating displacement based on bore and stroke

If the dimensions are known but not the displacement, a calculation tool will calculate it for you. The displaced volume of a cylinder is the product of the cross-sectional area of the bore and the stroke.

V_{\mathrm{cyl}} = \frac{\pi B^2}{4} \times S \qquad D = n_{\mathrm{cyl}} \times V_{\mathrm{cyl}}

With a bore of 85 mm and a stroke of 97 mm, the displacement volume is 550.4 cc, so the engine's capacity for four cylinders is 2201.7 cc. The manufacturer usually rounds this up to 2.2 liters. Therefore, calculated values often do not exactly match those on the trunk lid.

Common Mistakes

The most common mistake is to use the displacement volume of a single cylinder instead of the total engine displacement. The formula requires the total displacement; using the displacement of a single cylinder in an V8 will overestimate the average piston effective pressure (BMEP) by a factor of eight.

Another common mistake is to set n incorrectly. If you set a two-stroke engine as four stroke the result will be doubled. This error is easy to make because most items are defaulted to four stroke.

Originally the maximum torque was to be used at points where it is needed. The use of the maximum power output instead of the maximum torque is a more serious error. The BMEP (Brake Mean Effective Pressure) does not reach its highest value where the power has its peak, but rather where the torque reaches its peak. Therefore engines whose power is indicated by their power peak always appear to be somewhat worse than they actually are.

The comparison of engines from different manufacturers is the most serious mistake. The comparison between diesel and petrol engines, turbocharged and naturally aspirated engines as well as methanol and petrol-driven engines is pointless because these engines have to perform different tasks.

Frequently asked questions

What is average effective braking pressure?: The BMEP is the average pressure acting on the piston and producing the torque that is actually measured by a dynamometer. It is not a measurable pressure but rather a number to standardize comparisons. It is valuable because it allows engines of different sizes to be compared on the same scale.
What is the formula for BMEP?: BMEP = 2 x π x n x T / D, where T is the brake torque, D is total displacement and n is crankshaft revolutions per expansion stroke. For four-stroke engines this is 2, for two-stroke engines it's 1. In yard-pound units the same relationship can be simplified to: BMEP (psi) = 150.8 x Torque in pound feet / Displacement in cubic inches, for four-stroke engines.
What are good values for brake mean effective pressure (BMEP)?: Most modern unboosted road-going gasoline engines have a BMEP of about 11 to 13 bar (about 160 to 190 psi). High performance street engines can reach up to 14 bar, while race engines such as those in Formula One or NASCAR often see values from 15 to 16 bar. Values above about 17 bar usually indicate a turbocharged engine, diesel engine, or an engine with fuel that contains its own oxygen.
Why doesn't the BMEP depend on engine speed?: The speed is balanced in the calculation process. The power is the product of torque and speed, and work per cycle results from dividing the power by the ignition frequency. Ignition frequency is also proportional to the speed. As the remaining value represents the work per cycle and cylinder content, data at 2000 rpm can be directly compared with data at 7000 rpm, provided that the torque was correctly measured.
Can we compare engines with turbochargers to aspirated engines?: A direct comparison is not possible. Supercharged engines pump more air into the cylinder due to their higher volume of air, so BMEP generally increases proportionally with the boost pressure ratio. When the supercharger function is enabled, the calculation tool divides the BMEP by this pressure ratio to bring the engine onto a scale that is closer to a naturally aspirated engine. This is not an exact correction but a plausibility check.
What is the difference between BMEP, IMEP and FMEP?: IMEP is derived from the pressure-time curve in the cylinder and represents work done by combustion. BMEP is derived from torque at the crankshaft and represents power output. The difference between these two values is FMEP. This corresponds to the pressure representing all losses of work due to friction, pumping loss, and the force required to drive the engine itself. The quotient of BMEP divided by IMEP gives the mechanical efficiency.
Does a higher BMEP mean a more efficient engine?: It means higher power per displacement but is not the same as thermal efficiency. It's possible to increase the BMEP by boosting or using a richer mixture while consuming more fuel per work done. The BMEP measures the workload on the displacement and not how efficiently the fuel was used.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Mean effective pressure
Definition of MEP, BMEP and IMEP, the derivation from work per cycle, and the revolutions-per-power-stroke factor.
EPI Inc: Brake Mean Effective Pressure, an important performance yardstick
Derivation of the 150.8 and 75.4 imperial constants, plus measured BMEP figures for aircraft, Formula 1 and NASCAR Cup engines.
x-engineer.org: Mean effective pressure (MEP)
IMEP, BMEP and FMEP from first principles, friction torque, mechanical efficiency and a fully worked bore-and-stroke example.
SAE International: J1349 Engine Power Test Code, Spark Ignition and Compression Ignition
The standard reference conditions that published torque and power figures are corrected to before any BMEP comparison is meaningful.