Data Source and Methodology
This calculator uses the standard, universally accepted engineering formula for converting torque and RPM to horsepower. This formula is derived from the definition of horsepower (1 HP = 33,000 ft-lb/min) and is consistent with industry standards such as **SAE J1349 (Engine Power Test Code)**.
All calculations are based strictly on the formulas provided by this standard.
The Formulas Explained
The relationship between horsepower, torque, and RPM is fixed by a mathematical constant: 5252. This number is derived from the conversion of units (explained in the FAQ below).
The three variations of the formula are:
Glossary of Variables
- Horsepower (HP)
- A measure of the rate at which work is done. In automotive terms, it's a measure of an engine's maximum power and often correlates with a vehicle's top speed.
- Torque (lb-ft)
- A measure of rotational force (specifically, pound-feet). In automotive terms, torque is the "grunt" or "pulling power" of an engine. It's what gets the vehicle moving from a stop and what you feel as acceleration.
- Engine Speed (RPM)
- Stands for Revolutions Per Minute. This is the speed at which the engine's crankshaft is rotating.
How It Works: A Step-by-Step Example
Let's say a performance engine is rated by the manufacturer as producing 400 lb-ft of torque at 5,000 RPM. We want to find its horsepower at that specific point.
- Select the formula: We want to find HP, so we use: $HP = \frac{Torque \times RPM}{5252}$.
- Input the values: $HP = \frac{400 \times 5000}{5252}$.
- Calculate the top half: $400 \times 5000 = 2,000,000$.
- Divide by the constant: $HP = \frac{2,000,000}{5252}$.
- Final Result: $HP \approx 380.8 HP$.
This means that at 5,000 RPM, that engine is producing 380.8 horsepower.
Frequently Asked Questions
Why the number 5252?
The constant 5252 is the result of converting units. One horsepower is defined as 33,000 ft-lb of work per minute. An engine's speed is in revolutions per minute. To get from 'revolutions' to 'ft-lb per minute', we use radians (2π radians per revolution). The math is: $\frac{33,000 \text{ ft-lb/min}}{2\pi \text{ rad/rev}} \approx 5252.1$. This constant correctly standardizes the units in the formula.
Do horsepower and torque always cross at 5252 RPM?
Yes, mathematically, if torque is measured in lb-ft and horsepower is calculated using the standard formula, the HP and torque values will be identical at 5252 RPM. At this speed, $\frac{Torque \times 5252}{5252} = HP$, which simplifies to $Torque = HP$. Below 5252 RPM, the torque value will be numerically higher than the HP value. Above 5252 RPM, the horsepower value will be higher.
What is more important: horsepower or torque?
Neither is 'more important'; they describe different things. Torque is the raw twisting force (the 'grunt' or 'pull') available at the crankshaft. It's what gets the car moving and what you feel as acceleration. Horsepower is the *rate* at which that torque can be applied (Torque × Speed). High torque at low RPM is great for towing. High horsepower at high RPM is great for high top speeds.
Does this formula work for electric motors?
Yes, the physics and the formula are identical for any rotating motor, whether it's an internal combustion engine, an electric motor, or a steam turbine. As long as you measure the torque output (in lb-ft) and the rotational speed (in RPM), this formula will correctly calculate the horsepower.
What about other units like kW or N·m?
This calculator is specifically designed for the imperial units common in the United States: horsepower (HP) and pound-feet (lb-ft). A different constant is required for metric units. The formula using kilowatts (kW) and Newton-meters (N·m) is: $kW = \frac{Torque_{N \cdot m} \times RPM}{9549}$.
Tool developed by Ugo Candido. Automotive engineering content reviewed by the CalcDomain Editorial Board.
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