A worked example: 2 bar and 30 PSI for tire pressure
Running 2 bar through the pressure converter's real formula, converting to PSI, returns 29.007548 PSI — close to a typical passenger-car tire spec. Running the reverse direction, 30 PSI converted to bar, returns 2.068427 bar. Both numbers describe pressure in the same physical range; they just come from a placard printed in different regions' preferred unit.
The formula: multiply by the from-unit-to-pascal factor, divide by the to-unit factor
The converter treats pascals as the base unit and stores every other pressure unit as a factor of one pascal: 1 bar = 100,000 Pa exactly, and 1 PSI = 6,894.757293168361 Pa. A conversion is amount × (from-unit-to-pascal factor) ÷ (to-unit-to-pascal factor). For 2 bar to PSI, that's 2 × 100,000 ÷ 6,894.757293168361, which works out to 29.007548 — matching the converter's actual output exactly.
A second example: 1 atmosphere to PSI, and blood pressure in pascals
The same formula handles the converter's other units without any special-casing. 1 atmosphere (defined as exactly 101,325 Pa) converts to 14.695949 PSI — a figure often quoted as the baseline for sea-level air pressure. A typical systolic blood-pressure reading of 120 mmHg converts to 15,998.68649 Pa using the mmHg factor of 133.322387415 Pa, showing the identical base-pascal mechanism working just as well for a medical reading as it does for a tire gauge.
Why converting through a single base unit matters
Storing every pressure unit as a factor of pascals — rather than writing a separate formula for every possible pair of units — is what lets one converter handle pascals, bar, atmospheres, PSI, and mmHg without seven-choose-two custom conversions. Adding a new pressure unit in the future only requires one new factor, not a formula for every existing unit it might convert to or from.