Pressure, Angle, and Force: The Engineering Conversions

Pressure, angle, and force are the conversions of engineering drawings, tire gauges, and physics homework — and they are where two traditions collide: SI's pascals, radians, and newtons against the psi, degrees, and pounds-force that workshop gauges still display.

Pressure: many names for one kind of stress

Pressure is force spread over area, and the SI unit — one pascal — is one newton per square meter. Because real-world pressures span huge ranges, each industry kept the unit that fit its numbers:

1 bar  = 100,000 Pa      1 atm = 101,325 Pa
1 psi  = 6,894.757 Pa    1 torr = 1 mmHg = 133.322 Pa
1 hPa  = 1 mbar = 100 Pa 1 inH2O = 249.089 Pa

The near-miss between bar and atmosphere is a standing trap: 1 bar is 100,000 Pa while 1 atmosphere is 101,325 Pa, a 1.3% gap that accumulated from sea-level air pressure measured in the 17th century. Aviation weather reports pressure in hectopascals — the same number meteorology used to call millibars, which is why "1013 hPa" and "1013 mbar" name the identical standard pressure. Medicine kept torr and millimeters of mercury from the old mercury-column instruments: 760 torr is exactly one standard atmosphere. And HVAC engineers size ducts in inches of water, where a full atmosphere is a bit over 406 inH₂O.

Tire gauges: psi, bar, and the 14.7 baseline

One atmosphere equals 14.696 psi, and that number explains what a tire gauge actually reports: gauge pressure, measured above ambient air. A reading of 35 psi means the air inside pushes about 35 psi harder than the atmosphere outside — 35 psi converts to 2.41 bar, which is why European placards list 2.4 bar for the same tire. Absolute pressure sensors (used for altitude and weather) read the 14.7 psi atmosphere as roughly 1 bar instead. Confusing the two is the classic instrumentation bug.

Angle: degrees, radians, and the 400-gradian detour

Angles have three competing ways to divide one full turn:

1 turn = 360 degrees   = 2π radians ≈ 6.28319 rad
       = 400 gradians  = 1 turn

Degrees are ancient and convenient: 360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, and 12, which is why compass roses and protractors use it. Radians are the mathematician's choice — one radian is the angle whose arc length equals the radius (about 57.2958°), and 90° is π/2 rad. Gradians, the metric-era attempt at decimalization, split the right angle into 100, so 90° is exactly 100 grads; surveying in some countries still uses them. The everyday failure mode is software: Math.sin() and every major programming language expect radians, so passing 90 produces sin(90 rad) ≈ 0.89 instead of 1. The Angle Converter converts between degrees, radians, gradians, and turns, which makes checking those constants a two-second job.

Force: newtons, pounds-force, and the kilogram trap

Force is where the metric-imperial split gets conceptually dangerous, because everyday language says "this bag weighs 10 kg" — kilograms are mass, not force. The force-world equivalents:

1 N    = 1 kg·m/s²       (SI base)
1 kgf  = 9.80665 N       ("kilogram-force", 1 kilopond)
1 lbf  = 4.44822 N       ("pound-force")
1 dyn  = 0.00001 N       (CGS dyne)
1 pdl  = 0.138255 N      (poundal)

The kilogram-force is defined by standard gravity: 9.80665 m/s² is the agreed value of Earth's pull, so 1 kgf is the weight of a 1 kg mass on Earth. That is why 100 N is the weight of about 10.2 kg — and why a 10 kg bag pulls your hand with 98.07 N, not 10 N. On the imperial side, 1 lbf is 4.44822 N, so 1 N is only 0.225 lbf; a torque wrench set in lbf·ft and a spec sheet in N·m differ by the same factor. The dyne and poundal survive from older coherent unit systems (CGS physics and the old foot-pound-second system, respectively) — the Force Converter normalizes all of them to newtons.

How the three fit together

These units interlock: torque is force times lever arm (newton-meters or pound-feet), pressure is force over area (pascals are newtons per square meter), and rotating machinery connects them — a motor's rpm sets angular speed in radians per second, which with a torque gives mechanical power. That is why the same spec sheet will list motor speed in rpm alongside torque in N·m. The historical why behind these parallel systems is told in Why Two Measurement Systems; here the practical rule is simpler — pick one anchor unit (pascal, radian, newton), convert everything to it, do the arithmetic, and convert out.

Try it yourself

Three checks, one per family. In the Pressure Converter, enter 35 psi and confirm 2.41 bar; enter 1 atm and confirm 760 torr and 14.7 psi. In the Angle Converter, enter 1 radian and read 57.2958 degrees, then 90 degrees and read 100 gradians. In the Force Converter, enter 100 N and read 22.48 lbf and 10.2 kgf — the last number being the "weight" your hand already knows.