Micronewtons to Poundals: 1 µN equals 7.23301e-6 pdl. To convert micronewtons to poundals, multiply by 7.23301e-6 (pdl = µN × 7.2330e-6). For example, 10 µN = 7.23301e-5 pdl.
How to Convert Micronewtons to Poundals
To convert from micronewtons to poundals, multiply the value by 7.23301e-6. The conversion is linear, meaning doubling the input doubles the output.
Conversion Formula
- Micronewtons to Poundals:
pdl = µN × 7.2330e-6 - Poundals to Micronewtons:
µN = pdl ÷ 7.2330e-6
Micronewtons to Poundals Conversion Chart
| Micronewtons (µN) | Poundals (pdl) |
|---|---|
| 0.1 | 7.23301e-7 |
| 0.25 | 1.80825e-6 |
| 0.5 | 3.61651e-6 |
| 1 | 7.23301e-6 |
| 2 | 1.44660e-5 |
| 3 | 2.16990e-5 |
| 5 | 3.61651e-5 |
| 10 | 7.23301e-5 |
| 20 | 0.000145 |
| 25 | 0.000181 |
| 50 | 0.000362 |
| 100 | 0.000723 |
| 250 | 0.001808 |
| 1000 | 0.007233 |
Understanding the Units
What is a Micronewton?
A millinewton equals one thousandth of a newton.
Common contexts: precision instruments, biomechanics.
What is a Poundal?
A poundal equals approximately 0.138255 newtons — the force needed to accelerate one pound-mass by one foot per second squared.
Common contexts: absolute foot-pound-second system.
How to Convert Micronewtons to Poundals
To convert micronewtons to poundals, multiply by 7.2330 × 10⁻⁶, or equivalently divide by 138,255. The factor encodes the definition of the poundal as the force required to accelerate one avoirdupois pound at one foot per second squared: 1 pdl = 1 lb·ft/s² = 0.138255 N. Unlike the pound-force, the poundal does not depend on standard gravity — it is the "absolute" imperial force unit.
Conversion Formula
- Micronewtons to Poundals: pdl = µN × 7.2330 × 10⁻⁶
- Poundals to Micronewtons: µN = pdl × 138,255
- Scientific notation: 1 µN ≈ 7.2330 × 10⁻⁶ pdl
Derivation: 1 pdl = 1 lb · 1 ft/s² = 0.45359237 kg × 0.3048 m/s² = 0.138254954 N = 138,254.95 µN. Inverting gives 1 µN = 1 / 138,255 pdl ≈ 7.2330 × 10⁻⁶ pdl.
Common Conversions
| Micronewtons (µN) | Poundals (pdl) | Scientific Notation |
|---|---|---|
| 0.1 | 7.233 × 10⁻⁷ | 7.23 × 10⁻⁷ pdl |
| 1 | 7.233 × 10⁻⁶ | 7.23 × 10⁻⁶ pdl |
| 5 | 3.617 × 10⁻⁵ | 3.62 × 10⁻⁵ pdl |
| 10 | 7.233 × 10⁻⁵ | 7.23 × 10⁻⁵ pdl |
| 25 | 1.808 × 10⁻⁴ | 1.81 × 10⁻⁴ pdl |
| 50 | 3.617 × 10⁻⁴ | 3.62 × 10⁻⁴ pdl |
| 100 | 7.233 × 10⁻⁴ | 7.23 × 10⁻⁴ pdl |
| 500 | 3.617 × 10⁻³ | 3.62 × 10⁻³ pdl |
| 1,000 | 7.233 × 10⁻³ | 7.23 × 10⁻³ pdl |
| 5,000 | 3.617 × 10⁻² | 3.62 × 10⁻² pdl |
| 10,000 | 7.233 × 10⁻² | 7.23 × 10⁻² pdl |
| 50,000 | 3.617 × 10⁻¹ | 3.62 × 10⁻¹ pdl |
| 100,000 | 7.233 × 10⁻¹ | 7.23 × 10⁻¹ pdl |
| 138,255 | 1.000 | 1.00 × 10⁰ pdl |
Understanding the Units
What Is a Micronewton?
The micronewton (symbol: µN) is the SI newton scaled by the prefix micro (10⁻⁶). One micronewton equals one millionth of a newton — the force needed to accelerate a 1-mg mass at 1 m/s². It is the working unit for atomic force microscopy, MEMS actuator design, surface chemistry, microbalance metrology, and single-cell biophysics.
What Is a Poundal?
The poundal (symbol: pdl) is the absolute imperial force unit, defined as the force required to accelerate one avoirdupois pound (0.45359237 kg) at one foot per second squared (0.3048 m/s²): 1 pdl = 1 lb·ft/s² = 0.138255 N. It is the imperial counterpart of the SI newton and the CGS dyne — all three are "absolute" units that derive directly from F = ma without invoking standard gravity. Unlike pound-force (lbf), which is gravitational, the poundal is intrinsic to mass and acceleration.
Absolute vs Gravimetric Imperial Force
The imperial system has two coexisting families of force units:
- Absolute (F = ma): poundal (pdl). Independent of gravity.
- Gravimetric (weight): pound-force (lbf), ounce-force (ozf). Defined relative to g₀ = 9.80665 m/s² (or its imperial equivalent, 32.17405 ft/s²).
The relationship is 1 lbf = g₀ pdl ≈ 32.174 pdl. The two systems were proposed independently in the late 19th century; engineers overwhelmingly preferred lbf because it matched spring-scale readings.
Small-Force Reference Table
Mapping micro-scale forces into both µN and pdl:
| Source of Force | Approximate µN | Poundals |
|---|---|---|
| Single dust particle weight | ~0.01 µN | ~7.2 × 10⁻⁸ pdl |
| AFM cantilever bend (soft, 100 nm) | ~0.1 µN | ~7.2 × 10⁻⁷ pdl |
| Mosquito body weight | ~15 µN | ~1.1 × 10⁻⁴ pdl |
| Sesame seed weight | ~30 µN | ~2.2 × 10⁻⁴ pdl |
| Single grain of rice | ~200 µN | ~1.4 × 10⁻³ pdl |
| Honeybee body weight | ~1,200 µN | ~8.7 × 10⁻³ pdl |
| Texture analyser gel threshold | ~5,000 µN | ~3.6 × 10⁻² pdl |
| Touchscreen finger tap (light) | ~100,000 µN | ~0.72 pdl |
| Lifting a US dime | ~22,300 µN | ~0.16 pdl |
| Tactile switch operating force | ~138,255 µN | ~1.0 pdl |
Micronewtons in Classical Mechanics and Ballistics Heritage
The poundal survives mainly in historical textbooks and older British physics curricula. Classical mechanics problems involving F = ma in imperial units use poundals so the equation stays dimensionally clean: a 5 lb mass accelerating at 3 ft/s² experiences 15 pdl of force. Switching to pound-force forces the substitution lbf = lb × (a / g₀), which complicates the algebra. The poundal was meant to clean that up — but most engineers chose to live with lbf and absorb the g₀ conversion factor.
In ballistics, momentum is sometimes tracked in lb·ft/s (foot-pounds-per-second), and the corresponding force unit — the poundal — keeps impulse calculations consistent. Modern ballistics, however, has largely migrated to SI: newtons, kg·m/s, and joules. The µN-to-poundal conversion is therefore primarily a translation tool for older datasets or for those occasional textbooks that still demand absolute imperial units.
Related Force Converters
- Micronewtons to Newtons — step up to the SI base unit
- Micronewtons to Pounds-force — gravimetric imperial cousin
- Micronewtons to Dynes — the CGS absolute counterpart
- Poundals to Newtons — pdl to SI base unit
- Newtons to Poundals — the canonical bridge
Brief History of the Poundal
The poundal was proposed in 1879 by James Thomson, an Irish engineer and brother of Lord Kelvin, as part of the wider push for "absolute" measurement systems where force is defined through F = ma rather than through weight under gravity. It paralleled the dyne (CGS, 1873) as the imperial-system equivalent absolute force unit. The General Conference on Weights and Measures (CGPM) eventually settled on the SI newton (1948), with no equivalent endorsement for the poundal.
Despite never gaining mainstream engineering adoption — most US and UK engineers continued to use pound-force — the poundal earned a place in British physics curricula and a handful of ballistics and propulsion handbooks. Today it is encountered mainly when reading pre-1970s technical literature, and the µN-to-poundal conversion exists primarily to translate that legacy material into modern SI units.