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# Position of the piston of engine with respect to crank angle

EmilyB.Position of the piston of engine with respect to crank angle

The **Position of the piston of engine with respect to crank angle** calculator computes the position of a piston pin from the crank center based on the rod length, the crank angle and the crank radius.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**r**) This is the crank radius - (
**A**) This is the crank angle - (
**l**) This is the rod length.

**Piston Position (x): **The position is returned in inches. However, this can be automatically converted to compatible units via the pull-down menu.

#### The Math / Science

The **Position of the piston of engine with respect to crank angle** expresses the motion of a non-offset piston connected to a crank through a connecting rod (as would be found in internal combustion engines). The formula for the piston position is:

`x=rcosA +sqrt(l^2-r^2sin^2A)`

where:

- x = piston position
- r = crank radius (distance between crank pin and crank center)
- A = crank angle (from cylinder bore centerline at TDC)
- l = rod length (distance between piston pin and crank pin)

## References

Wikipedia (https://en.wikipedia.org/wiki/Piston_motion_equations)

**Position of the piston of engine with respect to crank angle**, is used in 1 calculator.

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