Basic torque, Power–RPM, bolt torque, and unit converter — all in one tool
Torque is the rotational equivalent of linear force — it measures how much a force causes an object to rotate around a pivot point. Whether you are tightening a bolt on an engine, calculating the output of an electric motor, or designing a mechanical system, understanding torque is fundamental to engineering and everyday mechanical work. Our Torque Calculator combines four tools into a single tabbed interface: the Basic Torque calculator computes τ = F × r × sin(θ) and lets you solve for torque, force, or lever-arm distance; the Power–Torque–RPM tab handles the full power triangle with efficiency factors and AC motor synchronous speed; the Bolt Torque tab applies the standard T = K × F × d × (1 − l/100) formula with bolt-type and lubrication presets; and the Torque Converter tab instantly converts any torque value between N·m, lb·ft, lb·in, kgf·cm, kgf·m, and ozf·in. Torque is measured in Newton-meters (N·m) in the SI system, or pound-feet (lb·ft) in the US customary system. The two are related by: 1 lb·ft = 1.35582 N·m. In any rotational system, torque depends on three factors: the magnitude of the applied force, the perpendicular distance from the pivot (called the lever arm or moment arm), and the angle at which the force is applied relative to the lever arm. Maximum torque occurs at 90° — when the force is perfectly perpendicular to the lever arm. At 0° the force is aligned with the lever arm and produces zero torque. In motors and engines, torque and power are tightly related through rotational speed. The formula P (kW) = τ (N·m) × n (RPM) / 9550 applies in the metric system, while HP = τ (lb·ft) × n (RPM) / 5252 is the imperial equivalent. These constants derive from converting RPM to radians per second (multiply by 2π/60). Understanding this triangle lets engineers select the right motor for a given application — a high-torque, low-RPM motor is suited to heavy lifting, while a high-RPM, lower-torque motor is better for cutting or grinding. For fastening applications, the bolt torque formula T = K × F × d accounts for friction through the nut factor K (also called the torque coefficient). This dimensionless factor varies from 0.16 for cadmium-plated bolts to 0.30 for non-plated black-finish bolts. Lubrication further reduces the friction factor — SAE 40 oil can reduce required torque by over 50%. However, all bolt torque specifications carry an inherent ±25% uncertainty due to torque wrench calibration tolerances, which our calculator highlights prominently. This calculator is designed for mechanical engineers, automotive technicians, manufacturing professionals, DIY enthusiasts, and students studying physics or mechanical engineering. It replaces multiple separate tools and provides instant, accurate results with visual charts including a torque-speed curve for motor applications.
Understanding Torque
What Is Torque?
Torque (also called moment of force or rotational force) is a vector quantity that describes the tendency of a force to rotate an object around an axis, fulcrum, or pivot. The SI unit is the Newton-meter (N·m). In physics, torque τ equals the cross product of the position vector r and the force vector F: τ = r × F. For practical calculations with scalar values, this reduces to τ = F × r × sin(θ), where θ is the angle between the force vector and the lever arm. A common analogy is a wrench tightening a bolt: a longer wrench handle (greater r) requires less force to achieve the same torque. This is why breaker bars are longer than standard ratchets.
How Is Torque Calculated?
The basic torque formula is τ = F × r × sin(θ). F is the applied force in Newtons (or lbf), r is the perpendicular distance from the pivot point to the line of action of the force in meters (or feet), and θ is the angle between the force and the lever arm — at 90° this equals 1, giving maximum torque. For power-torque-RPM calculations, the metric formula is τ (N·m) = P (kW) × 9550 / n (RPM). The constant 9550 comes from (60 × 1000) / (2π) ≈ 9549.3, rounding to 9550. For bolt torque, T = K × F × d × (1 − l/100) where K is the nut factor, F is clamping force, d is bolt diameter, and l is lubrication reduction percentage.
Why Does Torque Matter?
Torque is critical in virtually every mechanical system. In automotive engineering, engine torque determines towing and acceleration capability — high torque at low RPM is essential for trucks and heavy vehicles. In manufacturing, precise bolt torque ensures joint integrity and prevents loosening from vibration or fatigue. Over-torquing can strip threads or crack components; under-torquing leads to joint failure. In electric motors, the rated torque determines the maximum load the motor can drive without overheating. In robotics and servo systems, torque specifications determine what payloads a joint can lift or hold. For everyday applications, understanding torque helps you choose the right tools and apply the correct tightening force.
Limitations and Accuracy
All torque calculations carry inherent assumptions and limitations. The basic formula τ = F × r × sin(θ) assumes a rigid lever arm, a point force application, and no friction at the pivot. Real systems have material flexibility, distributed loads, and friction losses. For bolt torque, the nut factor K is an empirical average — actual values vary by surface condition, lubrication distribution, thread quality, and bolt material. Industry standards acknowledge ±25% accuracy for torque wrench applications, meaning a target of 50 N·m could produce actual clamp loads anywhere from 37.5 to 62.5 N·m. Motor efficiency η also varies with load and temperature. For safety-critical applications, always consult manufacturer specifications and relevant engineering standards (e.g., ISO 16047 for fastener torque).
How to Use the Torque Calculator
Choose Your Calculator Mode
Select one of four tabs at the top: Basic Torque (τ = F × r × sin θ), Power–RPM (motor calculations), Bolt Torque (fastener tightening), or Unit Converter (torque unit conversions). Each tab has inputs specific to that calculation type.
Select What to Solve For
In Basic Torque mode, toggle between solving for Torque, Force, or Distance using the solve-for buttons. In Power–RPM mode, choose whether to find Torque, Power, or RPM. In Bolt Torque mode, switch between finding required torque or the resulting clamping force.
Enter Your Known Values
Type in the known quantities with appropriate units. For force, choose N, kN, lbf, or kgf. For distance, choose m, cm, ft, or in. Use the angle slider to set the force application angle — 90° gives maximum torque. For bolt torque, select the bolt type and lubricant to auto-fill K factor and lubrication percentage.
Read Results and Export
Results appear instantly as you type. The Basic Torque tab shows torque in N·m, lb·ft, lb·in, and kgf·cm simultaneously, plus a lever arm SVG diagram. The Power–RPM tab shows a torque-speed curve chart. Use the Copy, Export CSV, Print, or Share buttons to save and share your results.
Frequently Asked Questions
What is the difference between torque and force?
Force is a linear push or pull measured in Newtons (N) or pound-force (lbf). Torque is a rotational force — it measures how much a force causes rotation around a pivot point, measured in N·m or lb·ft. The key difference is that torque depends not just on the force magnitude but also on the distance from the pivot (lever arm) and the angle of application. You can increase torque by either applying more force or using a longer lever arm — this is why mechanics use long breaker bars for stubborn bolts.
What does the angle θ do in the torque formula?
The angle θ in τ = F × r × sin(θ) is the angle between the force vector and the lever arm. At 90°, sin(90°) = 1, so you get maximum torque — the force is perfectly perpendicular to the lever arm. At 0° or 180°, sin = 0, so no torque is produced at all — the force is aligned with the lever arm and only pushes or pulls along it. At 45°, you get only 70.7% of maximum torque. This is why pushing on a wrench at an angle is less effective than pushing straight perpendicular to the handle.
How do I convert torque to horsepower?
To convert torque to horsepower, use: HP = (Torque in lb·ft × RPM) / 5252. The constant 5252 comes from dividing 33,000 (foot-pounds per minute per horsepower) by 2π × 60 (converting RPM to radians per minute). In metric, the equivalent is: P (kW) = τ (N·m) × n (RPM) / 9550. For example, an engine producing 300 lb·ft at 5000 RPM generates approximately 285 HP. Use our Power–RPM tab to solve for any one of the three variables given the other two.
What is the nut factor (K) in bolt torque calculations?
The nut factor K (also called the torque coefficient or friction factor) is a dimensionless constant that accounts for the friction losses when tightening a bolt. It captures friction in the threads and under the nut face. Typical K values: 0.16 for cadmium-plated bolts (low friction), 0.20 for zinc-plated or dry uncoated bolts, and 0.30 for non-plated black-finish bolts (high friction). The full bolt torque formula is T = K × F × d, where F is the target clamping force and d is the nominal bolt diameter. Lubrication reduces effective friction by a percentage factor on top of K.
Why is there a ±25% warning on bolt torque results?
Torque wrenches are mechanical tools with inherent calibration tolerances. Even a well-calibrated click-type torque wrench has an accuracy of about ±4%, but the combined uncertainty from nut factor variability, surface condition, thread quality, lubrication distribution, and wrench calibration adds up to ±25% or more in the actual bolt preload (clamping force) achieved. This means a target of 50 N·m could result in actual preload anywhere from 37.5 to 62.5 N·m. For safety-critical joints (engine bolts, structural connections), always refer to manufacturer torque specifications and use calibrated tools.
What is synchronous motor speed and why does it matter?
Synchronous motor speed is the theoretical maximum speed of an AC induction motor based on its electrical supply frequency and number of poles: n_sync = 120 × f / poles. At 60 Hz with 4 poles, synchronous speed = 1800 RPM. Real motors run slightly slower than synchronous speed due to slip — typically 2–5% less. Synchronous speed is important because it sets the upper bound on motor speed without a variable frequency drive (VFD). Knowing synchronous speed helps you select motors for specific applications: a 2-pole motor at 60 Hz runs at ~3600 RPM (good for pumps), a 6-pole motor runs at ~1200 RPM (better for compressors).