What Is Torque?
Torque is a rotational force — a twist applied to an object around an axis. While a regular force pushes or pulls something in a straight line, torque makes something spin, turn, or rotate.
Every time you use a wrench, turn a steering wheel, pedal a bicycle, or open a jar lid, you are applying torque. The tighter a bolt needs to be, the more torque you need. The heavier the load a motor drives, the more torque that motor must produce.
Torque is the fundamental quantity that connects motors, gears, and mechanical output. Inside every electric linear actuator, a motor produces torque, gears multiply it, and a lead screw converts it into straight-line pushing or pulling force. Understanding torque is the first step to understanding how any motorized mechanical system works.
Torque Formula
The fundamental torque equation is:
Where:
- τ (tau) = torque, in N·m or ft·lb
- F = applied force, in N or lbf
- r = lever arm length (distance from the axis of rotation to where force is applied), in m or ft
- θ = angle between the force vector and the lever arm
When force is applied perpendicular to the lever arm (the most common and most efficient case), θ = 90° and sin(90°) = 1, so the formula simplifies to:
Worked example: You push with 20 lbs of force at the end of a 1.5-foot wrench handle, perpendicular to the wrench.
If the same 20 lbs is applied at 45° instead of 90°:
Applying force at an angle wastes some of it — only the perpendicular component creates torque. This is why you always push a wrench at 90° for maximum effect.
Torque Calculator (Force × Distance)
Enter the force applied and the lever arm length to calculate torque. Optionally enter the angle if force is not perpendicular.
Force:
Lever arm distance:
Angle (optional): ° (90° = perpendicular)
Torque vs. Force
People often confuse torque and force, but they are fundamentally different quantities:
| Property | Force | Torque |
|---|---|---|
| What it does | Pushes or pulls in a straight line | Twists or rotates around an axis |
| SI unit | Newton (N) | Newton-meter (N·m) |
| Imperial unit | Pound-force (lbf) | Foot-pound (ft·lb) |
| Formula | F = m × a | τ = F × r × sin(θ) |
| Depends on distance? | No | Yes — lever arm length matters |
| Real-world example | Pushing a box across a floor | Turning a wrench on a bolt |
The critical relationship: torque = force × distance. A small force applied far from the axis can produce the same torque as a large force applied close to the axis. This is the principle behind levers, wrenches, gears, and every actuator ever made.
Torque Units and Conversions
Torque is expressed in units of force × distance. The two most common systems are SI (metric) and Imperial (US customary). Here is a complete conversion reference:
| Unit | Abbreviation | Multiply by → N·m | Common Usage |
|---|---|---|---|
| Newton-meter | N·m | 1.0000 | SI standard, engineering worldwide |
| Foot-pound | ft·lb | 1.3558 | US automotive, construction |
| Inch-pound | in·lb | 0.11298 | Small fasteners, electronics |
| Kilogram-force meter | kgf·m | 9.80665 | Older metric practice |
| Kilogram-force centimeter | kgf·cm | 0.0980665 | Servo motors, small actuators |
| Ounce-force inch | ozf·in | 0.0070616 | Micro motors, hobby servos |
Quick conversions to memorize:
- 1 N·m = 0.7376 ft·lb
- 1 ft·lb = 1.3558 N·m
- 1 ft·lb = 12 in·lb
- 1 N·m = 8.8507 in·lb
Torque Unit Converter
Enter a torque value in any unit and instantly see all conversions.
Value:
Power, RPM, and Torque
Power, speed (RPM), and torque are locked together by the relationship:
In practical units:
Imperial: Torque (ft·lb) = HP × 5,252 ÷ RPM
Metric: Torque (N·m) = Power (W) × 9.5488 ÷ RPM
This tells you something critical: for a given power level, torque and speed are inversely related. If you want more torque from the same motor, you must accept less speed, and vice versa. This is exactly what gears do — they trade speed for torque (or torque for speed) while keeping power roughly constant (minus friction losses).
Worked example: A 0.5 HP electric motor spins at 3,000 RPM.
Now add a 50:1 gear reduction with 90% efficiency:
The gear train multiplied torque by 45× while reducing speed by 50×. This is the principle behind every linear actuator and geared motor system. For more on gear ratios, see our Gear Ratio Calculator & Guide.
Motor Torque Calculator (HP/Watts to Torque)
Enter motor power and speed to calculate the torque output.
Motor power:
Motor speed: RPM
Torque and Gear Ratio
Gears multiply torque at the cost of speed. The relationship is:
Output Torque = Input Torque × Gear Ratio × Efficiency
Output Speed = Input Speed ÷ Gear Ratio
A motor producing 1 N·m through a 60:1 gear reduction at 95% efficiency delivers 1 × 60 × 0.95 = 57 N·m at the output shaft, while speed drops from 3,600 RPM to 60 RPM.
Multi-stage gear trains multiply the ratios of each stage. A two-stage system of 5:1 and 12:1 gives 60:1 total. Efficiency compounds: 0.97 × 0.97 = 94.1%. See our Gear Ratio Calculator for a full interactive tool.
How Torque Becomes Linear Force: The Lead Screw
A lead screw (also called a power screw) converts rotational torque into straight-line linear force. This is the mechanism inside every electric linear actuator.
The formula to convert torque at the lead screw to linear force output is:
Where:
- F = linear force output (N or lbf)
- τ = torque at the lead screw shaft (N·m or ft·lb)
- η = screw efficiency (typically 0.25–0.50 for ACME screws, 0.85–0.95 for ball screws)
- L = lead — the distance the screw advances per revolution (m or ft)
Worked example: A gear train delivers 5 N·m of torque to an ACME lead screw with a 4 mm lead (0.004 m) and 35% efficiency.
This is how a small motor producing less than 1 N·m of torque can generate hundreds of pounds of linear force — gear reduction multiplies the torque, and the lead screw multiplies it again while converting rotation to linear motion.
Lead Screw Torque-to-Force Calculator
Enter the torque at the lead screw and the screw parameters to calculate the linear force output.
Torque at lead screw:
Lead (advance per revolution):
Screw efficiency: % (ACME: 25–50% | Ball screw: 85–95%)
Torque Inside Linear Actuators
Every electric linear actuator follows the same torque chain from motor to output force:
Step 1: Motor torque. A small DC motor (typically 12V or 24V) spins at 3,000–6,000 RPM, producing 0.1–2 N·m of raw torque.
Step 2: Gear reduction. A spur or planetary gear train with a ratio of 20:1 to 100:1+ multiplies the motor torque by that ratio (minus friction losses). At 50:1 and 90% efficiency, 1 N·m becomes 45 N·m.
Step 3: Lead screw conversion. The geared output drives an ACME or trapezoidal lead screw. The screw pitch and efficiency convert the rotational torque into linear push/pull force. A 4 mm lead at 35% efficiency converts 45 N·m into approximately 24,700 N (5,500+ lbs) of theoretical force — though real actuators are designed well within safe operating limits.
This is why actuator specifications always list force (in lbs or N) rather than torque — the torque has already been converted to linear force by the time it reaches the actuator rod. For a deeper look at actuator internals, see our Inside a Linear Actuator guide.
Torque Inside Rotary Actuators
A rotary actuator outputs torque directly rather than converting it to linear force. The gear train multiplies the motor's torque, and the output shaft delivers that multiplied torque to whatever it needs to rotate — a valve, a joint, an antenna, or a robotic arm.
Rotary actuator torque ratings are specified at the output shaft. A rotary actuator rated at 20 N·m can exert 20 newton-meters of rotational force. The motor inside may only produce 0.5 N·m, but the gear train multiplies it by 40× (with efficiency losses).
Static vs. Dynamic Torque
Static torque (also called breakaway torque or starting torque) is the torque required to begin rotation from a complete standstill. It must overcome static friction (stiction) in bearings, gears, and the load itself.
Dynamic torque (also called running torque) is the torque required to maintain rotation at a given speed. Dynamic friction is always lower than static friction, so dynamic torque is less than static torque.
In actuators, this means:
- Startup current is higher than running current because the motor must produce extra torque to overcome stiction
- A loaded actuator may stall if the startup torque is not enough to overcome the load's static friction
- Oversizing your actuator by 1.5× the expected load ensures reliable startup under all conditions
For more on actuator duty cycle and thermal limits under varying loads, see our Duty Cycle Guide.
Torque and Mechanical Advantage
Torque is the rotational form of mechanical advantage. Anywhere you increase distance (lever arm, gear diameter, wrench length), you reduce the force needed to produce the same torque.
Practical examples:
- Longer wrench = less effort: A 2-foot breaker bar needs half the force of a 1-foot wrench to loosen the same bolt
- Larger gear = more torque: A driven gear with twice the diameter (or teeth) of the driver doubles the output torque while halving the output speed
- Finer lead screw = more force: A screw with 2 mm lead produces twice the linear force of a 4 mm lead screw at the same input torque (but extends half as fast)
Every stage of an actuator — motor, gear train, and lead screw — uses this principle to multiply a small motor's torque into hundreds of pounds of output force. Use our free calculators to size the right actuator for your application.
Common Torque Values Reference Table
| Application | Typical Torque | Notes |
|---|---|---|
| Hobby servo motor (SG90) | 0.18 N·m (25 ozf·in) | Micro robotics, RC models |
| Micro actuator motor (before gears) | 0.1–0.5 N·m | Multiplied 20–50× by gear train |
| Standard actuator motor (before gears) | 0.5–2 N·m | Multiplied 30–100× by gear train |
| Hand-tightening a jar lid | 1–3 N·m | Finger and wrist strength |
| Bicycle pedal (casual riding) | 10–40 N·m | Leg force × crank length |
| Car lug nut | 80–140 N·m (60–100 ft·lb) | Varies by vehicle manufacturer |
| Cordless drill (max) | 40–80 N·m | Impact driver: 150–250 N·m |
| Car engine (small 4-cylinder) | 150–250 N·m | At peak torque RPM |
| Car engine (V8 truck) | 500–700 N·m | At peak torque RPM |
| Industrial servo motor | 5–500 N·m | Robotics, CNC, automation |
| Wind turbine generator | 500,000+ N·m | Multi-megawatt systems |
Common Mistakes in Torque Calculations
- Confusing torque units with energy units: N·m (torque) and joules (energy) have the same dimensions but are different physical quantities. Torque is a rotational force; a joule is work done. Never interchange them.
- Ignoring the angle: If force is not perpendicular to the lever arm, you must multiply by sin(θ). Applying force at 30° delivers only 50% of the torque compared to 90°.
- Forgetting gear efficiency: No gear system is 100% efficient. Always multiply by the efficiency factor (typically 0.85–0.97) when calculating output torque through a gear train.
- Using stall torque as working torque: A motor's stall torque is the maximum torque at zero speed — the motor is locked and drawing maximum current. Operating at stall will burn out the motor. Working torque is typically 30–50% of stall torque.
- Mixing Imperial and metric: ft·lb and N·m are not interchangeable. Always convert before combining values from different sources. Use the converter above to avoid errors.
- Ignoring lead screw efficiency: ACME lead screws are only 25–50% efficient due to thread friction. Ball screws are 85–95% efficient. Using 100% in your calculation will dramatically overestimate force output.
Related Guides and Calculators
- Gear Ratio Calculator & Guide — how gears multiply torque and trade speed for force
- Linear Actuator Engineering Guide — complete reference for force, stroke, duty cycle, and sizing
- Inside a Linear Actuator — detailed technical breakdown of motor, gears, and lead screw
- Types of Electric Linear Actuators — standard, micro, track, and column comparison
- Duty Cycle Explained — thermal limits and motor protection
- IP Ratings Explained — environmental protection for outdoor applications
- Mounting Brackets Guide — clevis, L-bracket, and ball-joint options
- Wiring Diagram Generator — custom wiring diagrams for any actuator setup
- Lid and Hatch Calculator — force and stroke sizing for hinged applications
- Linear Motion Calculator — push/pull/slide sizing tool
- Full Calculator Suite — all FIRGELLI engineering tools
- 5 Steps Before Buying an Actuator — avoid common purchasing mistakes
- Shop Linear Actuators — browse all models by force, stroke, and speed
Frequently Asked Questions About Torque
What is torque?
Torque is a rotational force that causes an object to turn around an axis. It equals the applied force multiplied by the perpendicular distance from the axis of rotation (the lever arm). Torque is measured in newton-meters (N·m) or foot-pounds (ft·lb). While regular force pushes or pulls in a straight line, torque twists or rotates.
What is the formula for torque?
The basic torque formula is τ = F × r × sin(θ), where τ is torque, F is the applied force, r is the lever arm length (distance from the axis of rotation), and θ is the angle between the force and the lever arm. When force is applied perpendicular to the lever arm (the most common case), sin(90°) = 1 and the formula simplifies to τ = F × r.
What is the difference between torque and force?
Force is a push or pull along a straight line, measured in newtons (N) or pounds-force (lbf). Torque is a twisting or rotational force around an axis, measured in newton-meters (N·m) or foot-pounds (ft·lb). Torque equals force multiplied by the lever arm distance. You can have a large force with zero torque if the force passes directly through the axis of rotation.
How do you convert torque to linear force?
To convert torque to linear force through a lead screw (as used in actuators), use the formula: Linear Force = (2π × Torque × Efficiency) ÷ Lead. Lead is the distance the screw advances per revolution. This is how electric actuators convert a motor's rotational torque into hundreds of pounds of straight-line push or pull force.
How do you convert newton-meters to foot-pounds?
Multiply newton-meters by 0.7376 to get foot-pounds. For example, 100 N·m × 0.7376 = 73.76 ft·lb. To convert foot-pounds to newton-meters, multiply by 1.3558. For example, 100 ft·lb × 1.3558 = 135.58 N·m.
How do you calculate motor torque from horsepower and RPM?
Use the formula: Torque (ft·lb) = (HP × 5,252) ÷ RPM. In metric: Torque (N·m) = (Power in watts × 9.5488) ÷ RPM. For example, a 1 HP motor at 1,750 RPM produces 5,252 ÷ 1,750 = 3.0 ft·lb (4.07 N·m) of torque.
What torque does a linear actuator motor produce?
The small DC motors inside linear actuators typically produce 0.1 to 2 N·m of raw torque at the motor shaft. Gear reduction multiplies this by 20× to 100× or more, producing 5 to 100+ N·m at the lead screw. The lead screw then converts that rotational torque into linear forces of 50 to 2,000+ pounds, depending on the actuator model and gear ratio.
Why does a longer wrench require less force?
Because torque = force × distance. If you double the wrench length (lever arm), you only need half the force to produce the same torque. This is mechanical advantage in action — the same principle used in actuator gear trains, where a small motor force is multiplied through gears and a lead screw to produce large output forces.
What is the difference between static torque and dynamic torque?
Static torque is the torque required to start rotation from a standstill (also called breakaway torque). Dynamic torque is the torque required to maintain rotation at a given speed. Static torque is always higher than dynamic torque because static friction (stiction) must be overcome to initiate movement. In actuators, this means startup current is higher than running current.
How does gear ratio affect torque?
Output torque = input torque × gear ratio × efficiency. A gear ratio of 50:1 with 90% efficiency multiplies the motor's torque by 45×. However, output speed is reduced by the same factor (divided by 50). This is why high-force actuators are slower and low-force actuators are faster — the gear ratio trades speed for torque.
