Horsepower to Torque Calculator
This horsepower to torque calculator uses the formula HP = Torque × RPM / 5252 to solve for horsepower, torque (ft-lb or Nm), or engine speed (RPM). Choose what you want to find, enter the two known values, and get an instant result with unit conversions between HP, kW, ft-lb, and Nm.
Horsepower to Torque Calculator
Use the formula HP = Torque × RPM / 5252 to solve for horsepower, torque, or RPM. Select what you want to find, enter the two known values, and get instant results with unit conversions.
Frequently Asked Questions
What is the formula for horsepower and torque?
The formula is HP = Torque (ft-lb) × RPM / 5252. This means horsepower equals the torque in foot-pounds multiplied by the engine speed in RPM, divided by 5252. You can rearrange this to find torque (Torque = HP × 5252 / RPM) or RPM (RPM = HP × 5252 / Torque).
Where does the number 5252 come from?
5252 comes from converting between mechanical horsepower and rotational power. One horsepower equals 33,000 ft-lb per minute (Watt's definition). Dividing by 2π (radians per revolution) gives 33,000 / (2π) ≈ 5252.11. It is simply a unit conversion constant that appears whenever you mix feet-pounds and RPM with horsepower.
At what RPM are horsepower and torque always equal?
Horsepower and torque (in ft-lb) are always numerically equal at exactly 5,252 RPM. This is a mathematical identity that holds for every engine — if you read a dyno chart, the HP and torque curves will always cross at 5,252 RPM. Below that point, torque is numerically higher; above it, horsepower is higher.
How do I convert horsepower to kilowatts?
To convert mechanical horsepower to kilowatts, multiply by 0.7457. For example, 200 HP × 0.7457 = 149.1 kW. To convert back, divide by 0.7457 (or multiply by 1.341). Note that metric horsepower (PS) is slightly different: 1 PS = 0.7355 kW.
How do I convert foot-pounds to newton-metres?
To convert foot-pounds (ft-lb) to newton-metres (Nm), multiply by 1.3558. For example, 300 ft-lb × 1.3558 = 406.7 Nm. To convert Nm back to ft-lb, divide by 1.3558 (or multiply by 0.7376). Most European car specs list torque in Nm, while US specs typically use ft-lb.
What is the difference between horsepower and torque in a car?
Torque is the engine's rotational force — it determines pulling strength and acceleration from low speeds. Horsepower is the rate of doing work — it determines top-end performance and how fast the car accelerates at higher speeds. Torque peaks at lower RPM (especially in diesel engines), while horsepower peaks closer to the engine's redline. Both are equally important; torque determines feel, horsepower determines speed.
How do I calculate horsepower from torque and RPM?
Use the formula: HP = Torque (ft-lb) × RPM / 5252. For example, an engine producing 350 ft-lb of torque at 4,500 RPM generates HP = 350 × 4500 / 5252 ≈ 299.9 HP, roughly 300 HP. Our calculator handles this automatically — just select 'Find Horsepower', enter the torque and RPM, and get the result instantly.
Can I use this calculator for electric motors?
Yes. Electric motors follow the same physics — power equals torque times angular velocity. The formula HP = Torque × RPM / 5252 applies to any rotating machine. However, electric motors produce peak torque from 0 RPM, so you will often be solving for HP or RPM at a specific operating point rather than a peak value. The unit conversions (HP to kW, ft-lb to Nm) are especially useful since electric motor specs are usually given in kW and Nm.
Understanding Horsepower, Torque & RPM
The HP = Torque × RPM / 5252 Formula
Horsepower and torque are both measures of an engine's output, but they describe different aspects of performance. Torque is a rotational force — the twisting effort the engine produces — while horsepower measures the rate at which that work is done. They are related by engine speed (RPM) through a single formula:
Horsepower Formula:
HP = Torque (ft-lb) × RPM / 5252
- HP = Horsepower (mechanical horsepower)
- Torque = Rotational force in foot-pounds (ft-lb)
- RPM = Engine speed in revolutions per minute
- 5252 = The magic constant (explained below)
The formula can be rearranged to solve for any of its three variables:
Solve for torque:
Torque = HP × 5252 / RPM
Solve for RPM:
RPM = HP × 5252 / Torque
A useful rule of thumb: at exactly 5,252 RPM, horsepower and torque (in ft-lb) are always numerically equal. Below that RPM, torque exceeds horsepower; above it, horsepower exceeds torque. This crossover point is a direct consequence of the constant 5252.
Why 5252?
The constant 5252 comes from the definition of mechanical horsepower and the conversion between linear and rotational power. Here is the derivation:
1 HP = 550 ft-lb/s (Watt's original definition)
Power = Torque × Angular velocity
Angular velocity (rad/s) = RPM × 2π / 60
HP = Torque × RPM × 2π / (60 × 550)
HP = Torque × RPM / (60 × 550 / 2π)
60 × 550 / 2π = 33,000 / (2π) ≈ 5,252.11
James Watt defined one horsepower as 33,000 foot-pounds of work per minute (or 550 ft-lb per second), based on his observations of how much work a strong horse could sustain. Dividing 33,000 by 2π (the number of radians in a full revolution) gives approximately 5,252 — the constant used in every dynamometer reading today.
HP vs Torque Curves
On a standard engine dyno chart, torque and horsepower are plotted against RPM. Several important observations apply to almost every combustion engine:
Peak Torque Comes First
Torque typically peaks at a lower RPM than horsepower. A diesel engine might produce peak torque at 1,600–2,000 RPM, making it excellent for towing and low-speed pulling. A performance gasoline engine might peak torque at 4,000–5,000 RPM. The torque curve shape determines how the car feels when accelerating from low speeds.
The Crossover Point at 5,252 RPM
Because HP = Torque × RPM / 5252, the HP and torque curves will always cross at exactly 5,252 RPM — regardless of the engine. At this point, the numerical value of HP equals the numerical value of torque (in ft-lb). This is a mathematical identity, not a coincidence, and appears on every properly measured dyno chart.
Peak HP Comes After Peak Torque
Once torque starts falling, horsepower can still rise if the rate of RPM increase outpaces the torque drop. Horsepower peaks at the RPM where the torque is falling at a rate that exactly offsets the RPM gain. Beyond that point, both torque and horsepower fall together. This is why a typical performance engine makes peak HP close to its redline.
Real-World Example: 300 HP, 300 ft-lb Engine
If an engine makes 300 ft-lb of torque at 5,252 RPM:
HP = 300 × 5252 / 5252 = 300 HP
Exactly 300 HP — confirming the crossover rule. If the same engine still makes 300 ft-lb at 6,000 RPM (unlikely but instructive):
HP = 300 × 6000 / 5252 ≈ 342 HP
Unit Conversions (HP, kW, ft-lb, Nm)
The formula above uses US customary units (mechanical horsepower and foot-pounds). Metric equivalents use kilowatts (kW) and newton-metres (Nm). Here are the key conversion factors:
| From | To | Multiply by |
|---|---|---|
| Horsepower (HP) | Kilowatts (kW) | 0.7457 |
| Kilowatts (kW) | Horsepower (HP) | 1.3410 |
| Foot-pounds (ft-lb) | Newton-metres (Nm) | 1.3558 |
| Newton-metres (Nm) | Foot-pounds (ft-lb) | 0.7376 |
The metric equivalent of the formula uses kilowatts and newton-metres:
kW = Torque (Nm) × RPM / 9549
The constant 9549 ≈ 60,000 / (2π), derived from 1 kW = 1,000 W and the same angular velocity conversion.