Pound-force to poundals: where the 32.174 comes from
What this conversion does
It multiplies by 32.174, and that number is the entire story of these two units. Pound-force builds itself from a pound of mass and standard gravity; the poundal builds itself from the same pound and an acceleration of one foot per second squared. Divide 9.80665 by 0.3048 and 32.174 falls out. A push of 25 lbf is 804.35 pdl, the same push expressed in the unit that never mentions gravity.
One pound, two different accelerations
The poundal is the coherent unit of the foot-pound-second system: one pound of mass accelerated by one foot per second squared. It is defined without any reference to gravity, and that is what makes it clean in mechanics, because F = m·a needs no constant to make it balance. The pound-force takes the other road and folds the Earth's pull into the unit itself, so that a pound of mass resting on a table can be said to press with one pound-force.
Pound-force to poundals conversion table
Forces small enough to hold in your head alongside the arithmetic, so the 32.174 step can be checked by eye on every row.
| Pound-force (lbf) | Poundal (pdl) |
|---|---|
| 1 | 32.1740485564 |
| 10 | 321.740485564 |
| 50 | 1608.70242782 |
| 100 | 3217.40485564 |
| 500 | 16087.0242782 |
| 2000 | 64348.0971129 |
Gravity divided by a foot
Standard gravity is 9.80665 metres per second squared. The poundals unit of acceleration is one foot per second squared, which is 0.3048 of that. The quotient is 32.1740485564, and it is a pure number with no units left in it — a ratio between a gravity and a length, both of them fixed by definition. That is why the factor is neither 32 nor a rounded 32.2, but a value that can be written to ten digits and still be exact.
The poundal keeps gravity out of the sum
Carry the same mass to the Moon and the gravitational pull on it falls to about a sixth, but the poundal figure for a push you apply does not move at all: it counts mass and acceleration and hides no planetary constant inside. That is the practical difference between the two units, and the reason a mechanics text built around F = m·a reaches for the smaller, odder-looking one.
Frequently asked questions
Why is there a factor of 32.174 between pound-force and poundals?
Because each unit multiplies the pound by a different acceleration. Pound-force uses standard gravity, 9.80665 metres per second squared; the poundal uses one foot per second squared, or 0.3048. Divide the first by the second and 32.174 is what is left over.
Which of the two is the coherent unit for foot-pound-second work?
The poundal. In a coherent system no conversion factor appears anywhere in the equations, so F = m·a holds with mass in pounds, acceleration in feet per second squared and force in poundals. The pound-force is a gravitational unit bolted on afterwards, and using it forces a 32.174 into every calculation.
Is the poundal still used anywhere today?
Rarely in industry, occasionally in teaching. British and American textbooks of the mid twentieth century used it to keep mechanics free of the gravity constant, and a few aerodynamics texts kept the habit for years afterwards. It survives here because this pair illustrates what a coherent unit is better than any other.
Does the poundal change with local gravity?
No. It is defined by a mass and a distance and a time, with no gravitational constant anywhere in the definition, so a force in poundals means the same thing at the equator, at the poles and in orbit. The pound-force, by contrast, is pinned to standard gravity by definition wherever it is used.
What is one pound-force in poundals, in round numbers?
Roughly 32. Two pound-force is 64.35 pdl and ten pound-force is 321.74 pdl. The factor sits close to a round number, which is exactly why the remainder matters in a long calculation: 32.174 and not 32, with the extra 0.174 accumulating row after row.