Every engineer learns the formula early: HP = (Torque x RPM) / 5252. It appears in textbooks, motor spec sheets, and countless online calculators. Yet despite its simplicity, this formula breeds more confusion than almost any other in mechanical engineering.
The 5252 constant is not arbitrary. Understanding where it comes from reveals fundamental truths about rotational power that many engineers overlook.
Where 5252 Actually Comes From
The constant 5252 derives from unit conversion, specifically from James Watt’s original definition of horsepower.
Watt defined one horsepower as the ability to lift 33,000 pounds one foot in one minute. This gives us:
1 HP = 33,000 ft-lb/min
Torque, however, is measured in pound-feet (lb-ft), and rotational speed is measured in revolutions per minute (RPM). To convert rotational motion to linear work, we need to account for the circumference of rotation.
One revolution equals 2 pi radians. So the relationship becomes:
Power (ft-lb/min) = Torque (lb-ft) x RPM x 2 pi
To express this in horsepower:
HP = (Torque x RPM x 2 pi) / 33,000
Simplify: 33,000 / (2 x pi) = 5,252.11…
Rounded to 5252, this constant bridges the gap between rotational force and linear power. The math is exact. The confusion comes from how people apply it.
The Common Misconceptions
Misconception 1: Torque and Horsepower Are Independent
Many engineers treat torque and horsepower as separate characteristics that a motor “has.” In reality, if you know two of three values (torque, RPM, horsepower), the third is mathematically determined.
A motor cannot produce 100 lb-ft at 5000 RPM and only make 50 HP. The physics do not allow it. At those values:
HP = (100 x 5000) / 5252 = 95.2 HP
When spec sheets show different values than the formula predicts, it means the torque and power measurements were taken at different RPM points. This leads directly to the next misconception.
Misconception 2: Peak Torque and Peak Power Occur Together
On almost every motor, peak torque and peak horsepower occur at different RPM. For internal combustion engines, peak torque typically occurs at lower RPM than peak power. Electric motors often produce peak torque at or near zero RPM.
This is not a violation of the formula. It simply means the torque curve and power curve have different shapes.
Consider a motor that produces:
- 200 lb-ft at 3000 RPM = 114 HP
- 180 lb-ft at 5000 RPM = 171 HP
- 150 lb-ft at 6000 RPM = 171 HP
Peak torque (200 lb-ft) occurs at 3000 RPM. Peak power (171 HP) occurs higher in the rev range even though torque has fallen.
Misconception 3: The 5252 Crossover Point Is Significant
In horsepower versus torque graphs using lb-ft and HP on the same scale, the curves always cross at exactly 5252 RPM (assuming the motor reaches that speed). Some interpret this crossover as mechanically significant.
It is not. The crossover is purely an artifact of the unit conversion. At 5252 RPM, when torque equals X lb-ft, power equals X HP by mathematical definition. Change your units to Newton-meters and kilowatts, and the crossover point shifts to an entirely different RPM.
The crossover tells you nothing about the motor’s characteristics. It is a graphing curiosity, not an engineering principle.
Understanding Torque Curves
A motor’s torque curve reveals its true character far better than peak specifications.
Flat torque curves deliver consistent pulling power across the RPM range. Diesel engines and many electric motors exhibit this characteristic, making them well-suited for applications requiring steady load handling.
Peaky torque curves concentrate output in a narrow RPM band. High-revving gasoline engines often show this pattern, requiring careful gear selection to keep the engine in its power band.
Rising torque curves increase output as RPM climbs. Turbocharged engines before reaching peak boost and some electric motors under certain control strategies display this behavior.
For motor selection, the shape of the torque curve matters as much as the peak values. An application requiring consistent low-speed pulling power needs a different motor than one requiring brief bursts of high-RPM output.
Full Load Current and the Torque Connection
For electric motors, the relationship between torque and current adds another layer of practical importance.
Motor current draw relates directly to torque output, not power output. A motor producing high torque at low RPM draws substantial current even though it produces minimal horsepower at that speed.
The full load amperage (FLA) rating on a motor nameplate indicates the current draw when the motor produces rated torque at rated speed. This is critical for:
- Wire sizing: Conductors must handle full load current continuously
- Overcurrent protection: Circuit breakers and fuses must not trip during normal operation
- Voltage drop: Higher current means greater voltage drop over distance
- Starting current: Induction motors draw 5-8 times FLA during startup
The formula relating current to torque for three-phase AC motors:
Torque (lb-ft) = (HP x 5252) / RPM
And for current:
HP = (Voltage x Current x Efficiency x Power Factor x 1.732) / 746
Combining these relationships allows engineers to calculate expected current draw for any operating point on the torque curve.
Practical Applications
Motor Selection
When selecting a motor for an application, start with the required torque at the operating speed, not the horsepower. A conveyor belt starting under load needs high torque at zero RPM. A centrifugal pump needs power that increases with the cube of speed.
Calculate horsepower from your torque requirements using the 5252 formula, then add appropriate service factor.
Gearbox Ratios
Gear reduction multiplies torque while dividing speed. A 10:1 gearbox connected to a motor producing 50 lb-ft at 1750 RPM delivers 500 lb-ft at 175 RPM. The horsepower remains constant (minus efficiency losses), demonstrating that torque and speed trade off while power stays fixed.
Variable Frequency Drives
VFDs allow electric motors to operate across a range of speeds, but the available torque varies with frequency. Below base speed, most VFDs maintain constant volts-per-hertz, providing constant torque capability. Above base speed, voltage is maxed out, so torque falls as speed increases (constant power region).
Understanding this torque-speed relationship is essential for proper VFD application.
The Metric Equivalent
For those working in SI units, the equivalent formula uses different constants:
kW = (Torque in Nm x RPM) / 9549
The constant 9549 derives from the same principle: converting rotational units to linear power units. In this case, 60,000 / (2 x pi) = 9549.
Key Takeaways
The 5252 constant is not mystical. It is straightforward unit conversion from Watt’s 18th-century horsepower definition. Understanding its origin clarifies the relationship between torque, speed, and power.
Remember:
- Torque and horsepower are mathematically linked through RPM
- Peak torque and peak power occur at different speeds
- The 5252 RPM crossover point is graphically interesting but mechanically meaningless
- For electric motors, current relates to torque, not power
- The torque curve shape determines application suitability
Engineers who internalize these principles avoid common specification errors and make better motor selection decisions. The formula is simple. The understanding makes the difference.