How are F1 engines are so powerful?

F1 engines are powerful despite having a small displacement because of some of the reasons below :

1. Ultra Light Engine parts :

All the moving parts of the engine have an inertia associated with them . The lighter the parts are designed , the inertia of the system reduces and this helps to develop more power . The moving or reciprocating parts such as pistons , connecting rods , camshafts , crankshaft are made of alloys which reduce the weight without compromising on strength . Generally aluminium - chromium alloys are used .

2. Size optimization :

Along with using light materials , engineers also considerably reduce size which further contributed to reduction in mass and reduction in the inertia of the system . The image juxtaposes a normal road car piston to a formula 1 piston . The optimization in size is evident from the image. It is possible to do such things as long life of engine is not a parameter in Formula 1 . The engine is designed to last maximum for a season of 19-20 races with an average of about 600 km running per race .

3. High RPM :

The break horse power (BHP) produced by the engine is given by the formula :

BHP = 2*pi*N*T/60
where
N=RPM
T=Torque

So, naturally to produce more power you need either high torque or high RPM . In Formula 1 engine , both are increased to get maximum overall output .
In our road cars usually redline is around 3000-4000 RPM . Even in high end cars like Ferrari Berlinetta and Lamborghini Aventador the engine revs to around 8000-9000 RPM . But F1 engines are clocked at around 16000-18000 RPM range .

4. Stroke to Bore Ratio :

It is the ratio of length of travel of each piston from top dead centre to bottom dead centre divided by the diameter of the cylinder . Generally a Stroke to Bore ratio of about 0.8-1.2 gives optimum efficiency . This factor is dependent on Heat transfer of flame through cylinder , scavenging effects , detonation and knocking tendencies . 
In Formula 1 however , power is of supreme importance hence the engines have a Stroke-bore ratio in the range of 0.4-0.5 . This improves the power but reduces engine efficiency . Also , this increases tendency of detonation and especially knocking which is counter balanced by using High Octane Fuel .

5. Higher Injection Pressure :

In our normal cars it is close to 150 bar but in the recent formula 1 engine it is 500 bar . Higher Injection pressure again contributed to more effective burning in a short span of time , remember to have an engine running at 16000 RPM , combustion time per stroke is very less , therefore increase in injection pressure is must to achieve such high engine speeds .