Pascal's Principle Calculator
Enter input force and the input/output areas to compute the output force and pressure via Pascal's principle p = F/A (constant in a fluid).
Input Data
Results
At a glance:Pascal's principle (Pascal, 1653): a pressure change applied to an enclosed incompressible fluid is transmitted equally to every point of the fluid and the container walls. Therefore pressure is the same throughout: p = F_in/A_in = F_out/A_out, so the output force is F_out = F_in·(A_out/A_in). The force is amplified by the area ratio (at the cost of a proportionally larger input displacement, conserving work). This is the principle behind hydraulic brakes, lifts and presses. This tool computes F_out, the common pressure p and the force ratio from F_in and the two areas.
Formula
Pascal: p = F_in/A_in = F_out/A_out
F_out = F_in·(A_out/A_in)
$$P = \frac{F_1}{A_1} = \frac{F_2}{A_2}, \quad F_2 = F_1 \cdot \frac{A_2}{A_1}, \quad F_1 d_1 = F_2 d_2$$How to Use
- Enter input force F_in and the input/output areas.
- The calculator returns F_out, pressure p and force ratio.
Case Studies
Hydraulic lift
F_in = 200 N, A_in = 0.01 m², A_out = 0.5 m².
p = 200/0.01 = 20000 Pa, F_out = 20000×0.5 = 10000 N.
50× force amplification.
FAQ
Why is pressure the same everywhere?
In a static incompressible fluid, any pressure applied is transmitted undiminished (otherwise fluid would accelerate); so p is uniform at a given height.
How does this multiply force?
Same pressure acts on a larger output area, giving F_out = p·A_out > F_in when A_out > A_in — force gained, distance lost (work conserved).
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.