Mechanical efficiency = (output energy)/(input energy) .
It's typically stated as a percentage.
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Output equals efficiency times input; in formula, Ot = Ef x In and so In = Ot/Ef. To calculate the original input, divide the output by the efficiency.
Efficiency= Mechanical Advantage Speed ratio X100 Mechanical advantage divided by speed radio X (times) 100
Mechanical advantage=load/effort
The mechanical advantage of a pulley can be greater than 1.The efficiency cannot but that is a different matter.
Engine efficiency is increased though compression ratio by allowing a more thermodynamic energy to be converted into mechanical energy. Energy transfer is the key to efficiency.