Engine

                    Power                  
       
     
  Brake Mean Effective Pressure   Volumetric Flow Rate  
       
           
  Indicated Mean Effective Pressure   Friction Mean Effective Pressure  
           
           
Compression/Expansion Ratio   Combustion   Pumping Losses   Mean Piston Speed   Total Bore Area   Volumetric Efficiency
     
     
  Gas Dynamics  

As seen in volumetric flow rate, the volumetric efficiency is defined this way:

VE =
Qm
Qth
(1)

Where:

Qm = Measured volumetric flow rate (m³/s)
Qth = Theoretical volumetric flow rate (m³/s)

The theoretical volumetric flow rate (Qth) is more or less chosen arbitrarily, based on atmospheric air density. Because air is compressible, a volume does not limit the quantity of air that can be pushed in, especially when gas dynamics are considered.

So volumetric efficiency is not a true «performance» criteria for an engine because what counts is the air mass flow rate. With everything else equal, an engine with a large VE burns the same amount of fuel and gives the same power output than a larger engine with a smaller VE. But values do compare with similar engines.

Mathematically, only a complex gas dynamics analysis can give a good approximation of the volumetric efficiency, but here are some ballpark values:

Typical VE
intake & exhaust
tuning		VE
@ max power
None (2-stroke & Wankel)55%
None (4-stroke)75%
Mild intake tuning (4-stroke)80%
Mild intake & exhaust tuning (4-stroke)90%
Tuned95%
Fully tuned100%
Best110%

Note: Add 5% @ maximum torque.

forced
induction		VE
@ max power
Street (10 psi)135%
Racing (20 psi)165%
Top fuel dragster (45 psi)230%
Tractor pulling − Pro stock (115 psi)360%
Tractor pulling − Super stock (200 psi)485%

Note: For a forced induction, it is a quasi-adiabatic compression that can be approximated by
VEboost = VEun-boost (
boost gauge pressure
atmospheric pressure
+ 1 )
1/1.7

Sources:

An ordinary low-performance engine has a VE of about 75% at maximum speed; about 80% at maximum torque. A high-performance engine has a VE of about 80% at maximum speed; about 85% at maximum torque. An all-out racing engine has a VE of about 90% at maximum speed; about 95% at maximum torque. A highly tuned intake and exhaust system with efficient cylinder head porting and a camshaft ground to take full advantage of the engine's other equipment can provide such complete cylinder filling that a VE of a 100% − or slightly higher − is obtained at the speed for which the system is tuned.

For contemporary naturally-aspirated, two-valve-per-cylinder, pushrod engine technology, a VE over 95% is excellent, and 100% is achievable, but quite difficult. Only the best of the best can reach 110%, and that is by means of extremely specialized development of the complex system comprised of the intake passages, combustion chambers, exhaust passages and valve system components. The practical limit for normally-aspirated engines, typically DOHC layout with four or more valves per cylinder, is about 115%, which can only be achieved under the most highly-developed conditions, with precise intake and exhaust passage tuning. Generally, the RPM at peak VE coincides with the RPM at the torque peak. And generally, automotive engines rarely exceed 90% VE.

Typical numbers for peak Volumetric Efficiency (VE) range in the 95%-99% for modern 4-valve heads, to 88% - 95% for 2-valve designs. If you have a torque curve for your engine, you can use this to estimate VE at various engine speeds. On a well-tuned engine, the VE will peak at the torque peak, and this number can be used to scale the VE at other engine speeds. A 4-valve engine will typically have higher VE over more of its rev range than a two-valve engine.