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Rod ratio calculator

Enter stroke, rod length and rpm. You get the rod ratio, a chart of where the piston is at every crank angle, the mean and peak piston speed with the crank angle of the peak, and the piston acceleration at top and bottom dead center.

Crank and rod

Stroke

Enter a stroke greater than zero.

Rod length (center to center)

Enter a rod length longer than half the stroke.

Engine speed

rpm

Enter an rpm from 1 to 30,000.

Rod length is measured between the centers of the big end and the small end bores.

Piston position against crank angle

Your rodEndless rod (pure sine motion)

The dot marks 90° of crank rotation. With a real rod the piston is already past half stroke there; the shorter the rod, the further past.

What the inputs mean

Stroke: how far the piston travels, twice the crank throw.
Rod length: center to center, big end to small end.
Engine speed: used for piston speed and acceleration only. The ratio itself does not depend on rpm.

The formulas

rod ratio = rod length ÷ stroke
r = stroke ÷ 2,  l = rod length,  θ = crank angle after TDC
piston below TDC = r + l − (r × cos θ + √(l² − r² × sin² θ))
piston speed = ω × (r × sin θ + r² × sin θ × cos θ ÷ √(l² − r² × sin² θ)),  ω = 2π × rpm ÷ 60
acceleration at TDC = ω² × r × (1 + r ÷ l),  at BDC = ω² × r × (1 − r ÷ l)
mean piston speed = 2 × stroke × rpm ÷ 60

Piston position is exact crank and rod geometry. The speed line is its derivative. The calculator finds the peak speed numerically, by scanning the crank angle and then narrowing in on the highest point. Some texts quote the ratio as rod length over crank radius, which is twice the number; both are shown.

Worked example

Stroke 3.480 in, rod 5.700 in, 6,000 rpm.

Rod ratio: 5.700 ÷ 3.480 = 1.638 (3.276 against the crank radius).
The piston reaches half stroke at 81.2° after top dead center. At 90° it is 2.012 in down, 57.8% of the stroke.
Mean piston speed: 3,480 ft/min (17.68 m/s).
Peak piston speed: 5,717 ft/min (29.04 m/s) at 74.3° after top dead center, 1.64 times the mean.
Acceleration: 22,774 m/s² (2,322 g) at top dead center and 12,122 m/s² (1,236 g) at bottom dead center.
Largest rod angle: 17.8° from the cylinder axis.

What a different rod changes

With the same crank and a 6.000 in rod the ratio becomes 1.724. The rod angle drops to 16.9°, the peak speed moves to 75.0° at 5,693 ft/min, and the acceleration at top dead center falls to 2,295 g while bottom dead center rises to 1,263 g. The mean piston speed does not change at all: it depends only on stroke and rpm. The piston also spends slightly less time near bottom dead center, which moves the piston position at the intake valve closing point; the dynamic compression calculator shows how much. Whether any of this matters for your build depends on the whole engine, so treat the numbers as geometry to compare, not a verdict.

Related calculators

Work out the static ratio first with the compression ratio calculator, and the pressure ratio of a boosted engine with the boost calculator. The engine set also covers dynamic compression, volumetric efficiency, BMEP and turbo airflow and compressor map points.

Questions

How do you calculate rod ratio?

Divide the rod length (center to center) by the stroke. A 5.700 in rod on a 3.480 in stroke gives 5.700 ÷ 3.480 = 1.638.

Does rod ratio change piston speed?

Not the mean piston speed, which depends only on stroke and rpm: 3,480 ft/min for a 3.480 in stroke at 6,000 rpm. The peak speed changes a little: 5,717 ft/min with a 5.700 in rod and 5,693 ft/min with a 6.000 in rod.

Where is piston speed highest?

Before 90° of crank rotation, close to where the rod and crank throw are at a right angle. With a 3.480 in stroke and 5.700 in rod the peak is at 74.3° after top dead center.

Why is the piston past half stroke at 90° of crank rotation?

The rod tilts as the crank turns, which pulls the piston down further than the crank throw alone. With a 3.480 in stroke and 5.700 in rod the piston is 57.8% of the way down at 90° and reaches half stroke at 81.2°.