TorqueMath

Engine Displacement & Compression Calculator

Four-stroke, two-stroke, Wankel rotary and steam engines. Displacement, static, dynamic and trapped compression, port timing, piston and apex-seal speed, firing order spacing and balance for inline, V, VR, W, boxer and radial layouts.

TorqueMath.com · Engine Displacement & Compression Calculator
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Compression ratio

Everything that stays above the piston at top dead center (TDC) adds to the clearance volume.

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Hit a target compression ratio

: 1

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Head gasket thickness vs compression

Same engine, only the compressed gasket thickness changes. Quench = gasket + deck height.

How it is calculated

Displacement is the volume swept by the pistons (or by the rotor flanks). Compression ratio compares the largest and smallest volume of one working chamber.

Swept volume, piston Vs = π/4 × bore² × stroke V = Vs × cylinders (1 ci = 16.387 cc) Clearance volume Vc = chamber + dish + π/4·gasket bore²·gasket + π/4·bore²·deck Static compression CR = (Vs + Vc) / Vc Piston travel from TDC x(θ) = r + L − r·cos θ − √(L² − r²·sin² θ) r = stroke/2, L = rod Dynamic CR (4-stroke) (Vc + π/4·bore²·x(180° + IVC)) / Vc Trapped CR (2-stroke) (Vc + π/4·bore²·(stroke − exhaust port depth + deck)) / Vc Port duration 360° − 2·θopen, where x(θopen) = port depth − deck Wankel, per chamber Vh = 3·√3 · R · e · B housing: x = e·cos 3α + R·cos α, y = e·sin 3α + R·sin α Steam, double acting V/rev = (2·A − A_rod) · stroke MEP = p1·c·(1 + ln 1/c) − p_back Mean piston speed cm = 2 × stroke × rpm / 60

Firing interval: 720° / cylinders for four-strokes, 360° / cylinders for two-strokes. A V engine with shared crankpins fires evenly when the bank angle is a multiple of that interval (V8 at 90°, V12 at 60°, V10 at 72°); other angles need split crankpins. Rule-of-thumb limits: gasoline dynamic CR about 7.5–8.5 : 1 on pump fuel, trapped CR of two-strokes about 6–8 : 1, mean piston speed under 20 m/s for street engines, Wankel apex-seal speed under about 35 – 40 m/s.

Wankel displacement is quoted per chamber (Mazda 13B = 2 × 654 cc = 1308 cc). Because each rotor fires once per eccentric-shaft revolution, racing rules often count it twice, as a 2.6 L four-stroke. Steam figures are ideal-cycle values; real engines lose 15–30 % more steam to clearance, wire-drawing and cylinder condensation.

This calculator finds engine displacement and compression from bore, stroke and cylinder count, then goes further: static compression ratio from chamber, piston, gasket and deck volumes, dynamic compression from intake valve closing and rod length, two-stroke trapped compression and port timing, Wankel chamber volume and steam engine output. Engine builders, mechanics, car and motorcycle enthusiasts and engineering students use it to plan a rebuild, choose a head gasket or cam, or check whether a build will run on pump fuel. Results are shown in cc, liters and cubic inches.

Worked example: a 2.0 liter four-cylinder with 86 mm bore and stroke

  1. Swept volume per cylinder: π/4 × 8.6² × 8.6 cm = 499.6 cc. With four cylinders, displacement is 1998.2 cc, or 2.0 L and 121.9 ci (1998.2 / 16.387).
  2. Clearance volume: 40.3 cc combustion chamber + 4.0 cc piston dish + gasket π/4 × 8.7² × 0.07 = 4.16 cc + deck π/4 × 8.6² × 0.025 = 1.45 cc, for a total of 49.91 cc.
  3. Static compression ratio: (499.6 + 49.91) / 49.91 = 11.0 : 1.
  4. Dynamic compression: with a 139 mm rod and the intake valve closing at 50° ABDC, the piston is still 74.6 mm from top dead center when the valve shuts, so only π/4 × 8.6² × 7.46 = 433.3 cc is actually compressed. Dynamic CR = (49.91 + 433.3) / 49.91 = 9.7 : 1.
  5. Mean piston speed at 7800 rpm: 2 × 0.086 m × 7800 / 60 = 22.4 m/s (4400 ft/min).

The engine displaces 1998 cc (121.9 ci) with 11.0 : 1 static and 9.7 : 1 dynamic compression. That dynamic figure is above the usual 7.5–8.5 : 1 pump-fuel guideline for engines without direct injection, and 22.4 m/s piston speed is above the 20 m/s street guideline, so this is a high-octane, high-rpm build.

FAQ

How do I calculate engine displacement?

Displacement = π/4 × bore² × stroke × number of cylinders. Work in centimeters to get cc directly, or in inches to get cubic inches. Example: a small-block V8 with a 4.00 in bore and 3.48 in stroke gives 0.7854 × 4.00² × 3.48 × 8 = 349.8 ci, which is 5733 cc or 5.7 L (1 ci = 16.387 cc). The figure is the total volume the pistons sweep from bottom to top dead center and does not include the combustion chamber.

How do I calculate compression ratio?

Static compression ratio = (swept volume + clearance volume) / clearance volume, for one cylinder. Clearance volume is everything above the piston at top dead center: the head chamber volume, plus a piston dish (or minus a dome), plus the compressed head gasket volume (π/4 × gasket bore² × thickness), plus the deck volume if the piston sits below the block deck. With 499.6 cc swept and 49.9 cc clearance, CR = 549.5 / 49.9 = 11.0 : 1. A thinner gasket or milled head reduces clearance volume and raises CR.

What is dynamic compression ratio?

Dynamic compression ratio counts only the part of the stroke after the intake valve closes, because no real compression starts until then. Find the piston position at intake valve closing (from stroke, rod length and the closing angle in degrees after bottom dead center), compute the swept volume above that point and use it in place of the full stroke: DCR = (Vc + π/4 × bore² × x) / Vc. A cam with late intake closing lowers dynamic CR, which is why a long-duration cam allows more static compression without knock.

What compression ratio can I run on pump gas?

There is no single static number, because cam timing, chamber design, head material and cooling all matter. A common rule of thumb for gasoline engines without direct injection is a dynamic compression ratio of about 7.5–8.5 : 1 on pump premium, a little higher with aluminum heads and a fast-burning chamber. With mild street cams that usually corresponds to roughly 9.5–10.5 : 1 static. Modern direct-injection engines with knock sensors and fine ignition control run 12–13 : 1 static or more, because fuel injected into the cylinder cools the charge.

How is rotary (Wankel) engine displacement calculated?

For a Wankel, displacement is quoted per working chamber: Vh = 3√3 × R × e × B, where R is the rotor generating radius, e the eccentricity and B the rotor width. The Mazda 13B has R = 105 mm, e = 15 mm and B = 80 mm, giving about 654 cc per chamber, so 1308 cc for two rotors. Each rotor completes one power stroke per eccentric shaft revolution, so it does the work of a four-stroke twice its size, and racing rules often count a 13B as 2.6 L.

What is mean piston speed and why does it matter?

Mean piston speed is the average speed of the piston over a revolution: cm = 2 × stroke × rpm / 60. A 86 mm stroke at 7800 rpm gives 22.4 m/s (4400 ft/min). It is a better measure of mechanical stress and wear than rpm alone, because inertia loads on rods and bearings rise with the square of piston speed. Typical street engines stay under about 20 m/s, sporting engines reach 20–25 m/s, and Formula 1 engines have run above 25 m/s. Peak piston speed is roughly 1.6 times the mean.

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