Efficiency Formula for Mechanical Systems; Definitions and Calculations

Efficiency is important!

Efficiency is a very important term in different fields. There are lots of use for this word in different means. But here, we will explain the real meaning of efficiency from the viewpoint of efficiency calculations and efficiency formulas in science and engineering. You can find detailed information about this term here;

  • What is efficiency?
  • How to calculate efficiency?
  • What are the types of efficiency?

What is the Efficiency of a System?

From most of the useful systems that we make or build, we have some expectations. In other words, we give labor and work to obtain that system. And we expense our sources to work that system. In return for this, that system gives us a useful thing that we intend to take. So the efficiency of this system is the rate of what we are giving in total and what we are cultivating from that system.

Efficiency = Output/Input

It is a very useful term for most systems. From the viewpoint of engineering systems, we are using efficiency extensively. There are different efficiency values for different systems.

What are the Types of Efficiency?

To understand the efficiency term at the engineering level, you can check the types of efficiencies that are mainly used in engineering applications.

Combustion Efficiency Formula

Combustion efficiency for a engine cylinder.
Cylinder of an ICE.

There are lots of systems that work with the combustion of chemicals. From the automotive industry to the energy industry, the combustion of different fuels is very important. So combustion efficiency is a very important factor that people consider in these systems.

To calculate the combustion efficiency, we need to know the heating value of the fuel. The heating value of fuel is the total heat released when the amount of fuel is burned at room temperature. We add the total heat of the gases into the calculation of this value. So we calculate the combustion efficiency as;

Formula of combustion efficiency.

So engineers are trying to increase the combustion efficiency values of the systems that have combustion. For example, in internal combustion engines, combustion efficiency is very important. After that, if the combustion efficiency of an internal combustion engine, the fuel is fully burned inside the cylinders and the burnt gases are leaving the cylinders at room temperature. But it is not like this.

In combustion efficiency, there are two classifications; lower heating values and higher heating values of fuels.

Lower Heating Values of Fuels

The low heating values of fuels are the calculation of the heating value that water leaves the combustion environment as vapor form. So, the total efficiency of the system will be lower because an amount of heat stays in the water vapor. In general, water leaves from the engine in vapor form, and the efficiencies of internal combustion engines are calculated with the lower heating values of fuels.

Higher Heating Values of Fuels

The higher heating value of fuels is the heating value in which the water leaves the combustion environment in liquid form. So, the heat energy of the condensation of the water is used also in these processes. For example, we calculate the efficiencies of fuel furnaces with higher heating values of fuels.

Annual Fuel Utilization Efficiency

AFUE is very important for heaters.

This is another efficiency calculation for heating systems of residential and commercial buildings. In the annual fuel utilization efficiency, we use the external additional factors. These factors, heat losses of the walls, off-on heat loss, etc. The acronym AFUE is generally used in the systems.

For example for such heating systems, AFUE values can be high as 90%. This may seem very high if we compare it with the other combustion systems. But these values of efficiencies are obtained with the regeneration of the water vapor in burnt gases. These systems use heat inside the vapor to cool the water vapor down to 95°F. Also, these systems are regenerating the heat inside the flue gases to use to heat the required environment. In conventional heating systems, flue gases may be up to 390-752°F. But these new systems use this heat of the flue gases down to 90°F which is very low. So, AFUE values of these systems can be high as 90 percent.

Efficiency Formula of Power Plants

Image Source: BBC.

Power plants are a very important part of our society. They are producing the required energy and electricity to run the world. So the efficiencies of power plants are a very important part. In the calculation of the efficiency of a power plant, we need to look at the other important efficiency parameters.

The first important thing is the efficiency of the combustion in the power plant. We explained the combustion efficiency. In most, fossil-fueled power plants, the combustion of the fuel is a very important factor in the efficiency.

Thermal Efficiency

Also, the thermal efficiency of the power plant is very important. We calculate the thermal efficiency as the ratio of the total shaft work to the total heat input to the working fluid. Fluids are heated up to certain degrees to turn the turbines. There is a shaft between the turbines and generators. Generators produce electricity from this shaft work.

Thermal efficiency is a very important topic in thermodynamics. 

Generator Efficiency

Generator efficiency is also very important. We calculate the generator efficiency as the ratio of the mechanical power input to the electrical power output.

So we calculate to calculate the total efficiency of a power plant, we need to multiply these three efficiency values; generator efficiency, thermal efficiency, and combustion efficiency.

Other Important Aspects of Efficiency

If we take a look at the efficiencies of the combustion systems, power plants have generally 55-60% of total efficiencies. And automotive engines such as fuel engines have efficiencies of around 25-30%. This efficiency value for diesel engines is around 35-40%.

For example, efficiency calculations are also valid for other types of systems such as light bulbs. The output lumens are proportioned to the total electrical power to find the lighting efficacies.

Another example of efficiency is cooking appliances. For example the energy transferred from the food to energy consumed by the appliance is the ratio of the efficiency of a cooking appliance.

General Viewpoint of Mechanical Efficiency

We can generalize the mechanical efficiency term to the general mechanical devices. Because the term efficiency has a very basic logic. Efficiency means, the ratio of mechanical energy input to mechanical energy output.

Always, there are irreversibilities in mechanical systems. Because of these irreversibilities, there is the term ‘efficiency’. If the efficiency of a system is 60%, the total energy loss because of the irreversibilities is 40%. Engineers are trying to reduce this irreversibility.

If we adopt this efficiency to the mechanical systems, we can have different types of efficiencies also.

Efficiency Formula of Pumps and Turbines

Image Source: Wikimedia.

Pumps and turbines are very important fluid mechanics systems. Pumps and turbines are the reverse systems. So, we use pumps to increase the velocity, pressure, or elevation of the fluids. And we use turbines to obtain mechanical energy by using fluid energy. So, the efficiency calculations of the pumps and turbines are different from each other.

We can calculate the efficiency of pumps with the formula below;

pump efficiency formula.

So, we are giving mechanical energy with the shaft work to increase the fluid’s energy. Most of the irreversibilities of pump systems are frictional losses.

But the purpose of the turbines, extracting the energy of fluid into useful mechanical energy. So the efficiency formula for turbines;

turbine efficiency formula.

Efficiency Calculator for Pumps, Turbines, and Power Plants

You may find yourself calculating the efficiencies of different engineering systems such as turbines, power plants, or pumps. So, you can use the calculator below to calculate the efficiencies of different systems easily.

So, the use of the calculator is very simple. You need to select the system that you want to calculate the efficiency. These systems are; General Systems that you can make calculations whatever you want, turbines, pumps, and power plants. After selecting the system, you need to enter the required input and output energies of the system.

After that, click on the ‘Calculate!’ button to see the efficiency of the system. If you want to make further calculations, click on the ‘Reset’ button to re-enter the values.


Above all, efficiency term is a very general term. And it is very useful to explain it by giving real examples. Efficiency formulas of pumps, engines, and other systems are generally used in the sector and research and development activities.

Mechanicalland does not accept any responsibility of calculations made by users in calculators. A good engineer must check calculations again and again.

Also, you can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Also, we added a useful calculator to calculate the different efficiencies of systems.

Finally, do not forget to leave your comments and questions below about the efficiency term.

Your precious feedbacks are very important to us.


What does efficiency mean? 

As we stated above, efficiency is the ratio of the desired output to the given input to the system. So in terms of efficiency, it is very important to what you gave to the system and what you take from the system. This is the general viewpoint of efficiency.

Why efficiency is important? 

For the environment, we need to use our sources in a minimum way. Because of the irreversible side, the energy is generally harmful to nature. Think about the exhaust fumes. So, it will be better to have fewer exhaust fumes from an engine. If we increase the efficiency of the engine, we can obtain a less harmful system. The higher efficiency is better.

Why efficiency is less than 100?

Because of the rules of physics and thermodynamics, the efficiency can not be higher than 100. Because of the entropy laws, there are always irreversibilities. If there are irreversibilities, the efficiency will be lower than 100.

Does efficiency have a unit?

Efficiency is a unitless value. Because you are dividing the same values to calculate the efficiency. For example, we are dividing the energy values by each other to calculate the efficiencies of engineering systems.


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