Compression ratio is the ratio between the total or combined area above the piston at bottom dead centre (BDC.) and the un-swept or combustion area above the piston at top dead centre. (TDC)
To calculate this ratio use this formula: add the swept volume and the un-swept and divide by the un-swept volume. (sw + un-sw) ÷ un-sw = ratio : 1

Swept volume...... is the area through which the piston travels during one stroke. It is calculated by multiplying the area of the cross section of the bore by the length of the stroke.
The formula to calculate the swept volume of one cylinder is: Pi × r × r × stroke = the swept volume of a cylinder. (area of travel of the piston from BDC. To TDC.) or more simply:
3.142 × (½ the bore size) × (½ the bore size) × stroke = sw

Un-swept volume...... is the area above the piston at TDC where combustion takes place. This area is irregular in shape and has to be measured by the use of fluid and a burette. All areas including spark-plug cavity, pre-combustion chambers and compressed head-gasket thickness are included. Convex or concave piston crowns become part of the measurement calculation. No formula can exist for this calculation except to add and subtract the measurements made to parts of the combustion area with the piston at TDC.

Total engine capacity...... Is the measurement of the swept volume of all cylinders in an engine. e.g. a 173 cubic inch Holden red motor is a 6 cylinder with a bore diameter of 3.5 inches and a stroke of 3 inches. Using the same formula as for swept volume, multiply the answer by the number of cylinders. Check the calculation below.

3.142 × (½ the bore size) × (½ the bore size) × stroke × number of cylinders.
So using this formula for a Holden 173 we will re-check it's stated capacity.
3.142 × (3.5 ÷ 2) × (3.5 ÷ 2) × 3 × 6 = capacity
3.142 × 1.75 × 1.75 × 3 × 6 = 173.2 ci