How do you calculate horsepower from torque and RPM?

Horsepower (hp) = [Torque (lb·ft) × RPM] / 5252. In SI units, Power (Watts) = Torque (N·m) × [RPM × 2π / 60]. For example, an engine producing 400 N·m (295 lb·ft) of torque at 5,252 RPM generates exactly 295 hp (220 kW).

Why does horsepower equal torque at 5252 RPM?

In imperial units, 1 horsepower is defined as 33,000 ft·lb/min. Since one revolution covers 2π radians, dividing 33,000 by 2π yields 5252.11. Therefore, when rotating at 5,252 RPM, torque in lb·ft numerically equals horsepower.

Kilogram-force centimeter to Pound-force inch (kgf·cm to lbf·in) Converter

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Live Conversion • ISO 80000-4:2019 Certified

1 Kilogram-force centimeter = 0.86796166 Pound-force inch

1 kgf·cm = 0.867962 lbf·in • 1 lbf·in = 1.152125 kgf·cm

Decimals:

Certified Authority Value

0.86796166

lbf·in

From / Input

kgf·cm

Swap to Pound-force inch to Kilogram-force centimeter

To / Result

lbf·in

Quick Values:

1 kgf·cm 5 kgf·cm 10 kgf·cm 25 kgf·cm 50 kgf·cm 100 kgf·cm 250 kgf·cm 500 kgf·cm 1,000 kgf·cm

Conversion Formula

To convert Kilogram-force centimeter to Pound-force inch, multiply by 0.86796166

kgf·cm × 0.86796166 = lbf·in

Calculation: 1 kgf·cm × 0.86796166 = 0.86796166 lbf·in

Common Kilogram-force centimeter to Pound-force inch Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Kilogram-force centimeter (kgf·cm) and Pound-force inch (lbf·in).

Tap any row to calculate

Kilogram-force centimeter to Pound-force inch: Primary Direct Table (15 Steps)

Rule: 1 Kilogram-force centimeter is equal to 0.867962 lbf·in (Pound-force inch)

Kilogram-force centimeter to Pound-force inch Conversion Reference Table
Conversion & Equivalent Value	Scientific Notation
0.001 kgf·cm is equal to 0.000867962 lbf·in (Pound-force inch)	8.68 × 10⁻⁴
0.01 kgf·cm is equal to 0.00867962 lbf·in (Pound-force inch)	8.68 × 10⁻³
0.1 kgf·cm is equal to 0.0867962 lbf·in (Pound-force inch)	8.68 × 10⁻²
0.5 kgf·cm is equal to 0.433981 lbf·in (Pound-force inch)	4.34 × 10⁻¹
1 kgf·cm is equal to 0.867962 lbf·in (Pound-force inch)	8.68 × 10⁻¹
2 kgf·cm is equal to 1.735923 lbf·in (Pound-force inch)	1.736 × 10⁰
5 kgf·cm is equal to 4.339808 lbf·in (Pound-force inch)	4.34 × 10⁰
10 kgf·cm is equal to 8.679617 lbf·in (Pound-force inch)	8.68 × 10⁰
20 kgf·cm is equal to 17.359233 lbf·in (Pound-force inch)	1.736 × 10¹
25 kgf·cm is equal to 21.699042 lbf·in (Pound-force inch)	2.17 × 10¹
50 kgf·cm is equal to 43.398083 lbf·in (Pound-force inch)	4.34 × 10¹
100 kgf·cm is equal to 86.796166 lbf·in (Pound-force inch)	8.68 × 10¹
250 kgf·cm is equal to 216.990416 lbf·in (Pound-force inch)	2.17 × 10²
500 kgf·cm is equal to 433.980831 lbf·in (Pound-force inch)	4.34 × 10²
1000 kgf·cm is equal to 867.961662 lbf·in (Pound-force inch)	8.68 × 10²

Pound-force inch to Kilogram-force centimeter: Reciprocal Summary

Rule: 1 Pound-force inch is equal to 1.152125 kgf·cm (Kilogram-force centimeter)

Pound-force inch to Kilogram-force centimeter Conversion Reference Table
Reciprocal & Equivalent Value	Scientific Notation
1 lbf·in is equal to 1.152125 kgf·cm (Kilogram-force centimeter)	1.152 × 10⁰
5 lbf·in is equal to 5.760623 kgf·cm (Kilogram-force centimeter)	5.761 × 10⁰
10 lbf·in is equal to 11.521246 kgf·cm (Kilogram-force centimeter)	1.152 × 10¹
50 lbf·in is equal to 57.606231 kgf·cm (Kilogram-force centimeter)	5.761 × 10¹
100 lbf·in is equal to 115.212462 kgf·cm (Kilogram-force centimeter)	1.152 × 10²

View Complete 15-Row Pound-force inch to Kilogram-force centimeter Table

Real-World Context & Everyday Benchmarks

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To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Kilogram-force centimeter (kgf·cm) and Pound-force inch (lbf·in):

Kilogram-force centimeter References:

Robotics hobby RC digital servo motor stall torque rating 15 kgf·cm
Cordless electric household screwdriver maximum fastening torque 50 kgf·cm
Automotive power window electric regulator gear torque 80 kgf·cm

Pound-force inch References:

Electrical panel circuit breaker terminal screw tightening spec 35 lbf·in
Rifle scope optical mount ring clamp bolt tightening torque 18 lbf·in

Tap any benchmark above to automatically calculate its exact equivalent in Pound-force inch.

ISQ Dimension: [M L² T⁻²] Coherent SI Unit: newton meter (N·m) Classical Mechanics & Dimensional Metrology

How to Convert Kilogram-force centimeter to Pound-force inch

Converting Kilogram-force centimeter (kgf·cm) to Pound-force inch (lbf·in) is a core calculation in Torque and Moment of Force, which measures the rotational or twisting force acting upon an object about an axis, pivot, or fulcrum. This calculation navigates the boundary between the International Metric System (SI) and British Imperial / US Customary engineering standards. In contemporary metrology, Imperial units are defined in terms of exact SI standards via international agreements—notably NIST SP 811 and the 1959 International Yard and Pound Agreement. Exactly 1 Kilogram-force centimeter equals 0.867962 Pound-force inch, while 1 lbf·in equals 1.152125 kgf·cm.

Direct Factor1 kgf·cm = 0.867962 lbf·in

Inverse Ratio1 lbf·in = 1.152125 kgf·cm

Conversion ScaleMetric SI to British Imperial / US Customary Bridge

First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (newton meter (N·m)) without arbitrary rounding:

V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)

Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)

1. Source SI Bridge (k_source):1 kgf·cm = 0.0980665 newton meter (N·m)

2. Target SI Bridge (k_target):1 lbf·in = 0.112985 newton meter (N·m)

Step-by-step substitution for Kilogram-force centimeter → Pound-force inch:V(lbf·in) = V(kgf·cm) × ( 0.0980665 / 0.112985 ) = V(kgf·cm) × 0.867962

Mathematical FormulaValue in Pound-force inch = Value in Kilogram-force centimeter × 0.86796166Direct computational formula applied for standard conversion.

Worked Example

To convert 120 Kilogram-force centimeter (kgf·cm) to Pound-force inch (lbf·in): multiply 120 by 0.867962 to get 104.155399 lbf·in. At an industrial engineering scale, 5000 kgf·cm converts to 4339.808311 lbf·in.

Inverse check: 1 lbf·in = 1.152125 kgf·cm.

Understanding Kilogram-force centimeter and Pound-force inch

Domain Metrology & Engineering Applications

Governing Law & Equation

Rotational Moment Vector Cross Product (τ = r × F)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using flanged rotary torque transducers, calibrated digital torque wrenches, and engine dynamometers.

Primary Industry Sectors

Applied across automotive powertrain calibration, wind turbine gearboxes, precision aerospace bolted assembly, and industrial pumps under international metrology standard ISO 80000-4:2019, NIST SP 811.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering Reference	Reference Value	Converted to Pound-force inch
Robotics hobby RC digital servo motor stall torque rating	`15 kgf·cm`	`13.019425 lbf·in`
Cordless electric household screwdriver maximum fastening torque	`50 kgf·cm`	`43.398083 lbf·in`
Automotive power window electric regulator gear torque	`80 kgf·cm`	`69.436933 lbf·in`

Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-4:2019, NIST SP 811 and the BIPM SI Brochure (9th Edition). Governed by Rotational Moment Vector Cross Product (τ = r × F) under ISO 80000 dimensional vector [M L² T⁻²].

Multi-Variable Engineering Bridge Drivetrain Dynamics & Shaft Power

Rotational Power & Motor Torque Bridge (kW • Horsepower • N·m • lb·ft • RPM • Rad/s)

Bridge rotational torque [M L² T⁻²] and shaft mechanical power [M L² T⁻³] across electric motors, engines, and gearboxes via rotational shaft dynamics P = τ × ω.

Input Shaft Torque (τ): kgf·cm

Select Shaft Operating Speed (RPM): 188.5 rad/s (from RPM)

Coupling: P = τ × ω

Forward Reverse

Live Calculated Bridge Equivalent:

1 kgf·cm at 1,800 RPM (4-Pole 60Hz US Industrial Motor) = 0.01849 kW

Equals 0.02479 hp • 0.02513 PS / cv • 18.4855 W

IEC Motor Standard

0.01849

Kilowatts

NEMA & Automotive

0.02479

Mechanical Horsepower

DIN Automotive

0.02513

PS / cv

Metric Horsepower

SI Standard

18.4855

Watts

Grid Turbines

1.848554 × 10⁻⁵

Megawatts

Imperial Power

13.6342

ft·lb/s

Foot-Pounds per Second

Step-by-Step Numerical Derivation Proof View Derivation

1. Normalize Input to SI Base Unit (N·m):
τ = 1 kgf·cm × 0.0980665 = 0.0980665 N·m
2. Apply Engineering Parameter (ω):
Selected condition: 1,800 RPM (4-Pole 60Hz US Industrial Motor) at ω = 188.5 rad/s (from RPM)
3. Execute Governing Physical Law in SI Units:
P = τ × ω = (0.0980665) × (188.5) = 18.485535 W
4. Convert to Standard Engineering Units:
• kW: 18.485535 × 0.001 = 0.01849 kW (Kilowatts) • hp: 18.485535 × 0.001341 = 0.02479 hp (Mechanical Horsepower) • PS / cv: 18.485535 × 0.00136 = 0.02513 PS / cv (Metric Horsepower) • W: 18.485535 × 1 = 18.4855 W (Watts) • MW: 18.485535 × 1 × 10⁻⁶ = 1.848554 × 10⁻⁵ MW (Megawatts) • ft·lb/s: 18.485535 × 0.7376 = 13.6342 ft·lb/s (Foot-Pounds per Second)

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Engineering Substance / Operating Standard	Parameter Value (rad/s (from RPM))	Reference State / Condition	Typical Industrial & Engineering Application
500 RPM (Slow Agitator / Marine Diesel)	`52.36`	ω = 500 × 2π / 60	Industrial mixer, pump jack & slow diesel output
1,000 RPM (Low-Speed Machine Tool Spindle)	`104.72`	ω = 1000 × 2π / 60	Heavy lathe chuck & milling arbor
1,500 RPM (4-Pole 50Hz AC Induction Motor)	`157.08`	Synchronous 50Hz 4-pole	European standard industrial electric motor
1,800 RPM (4-Pole 60Hz US Industrial Motor)	`188.5`	Synchronous 60Hz 4-pole	North American NEMA electric motor standard
3,000 RPM (2-Pole 50Hz Generator / Turbine)	`314.16`	Synchronous 50Hz 2-pole	European 2-pole synchronous power generation
3,600 RPM (2-Pole 60Hz US Generator)	`376.99`	Synchronous 60Hz 2-pole	North American 2-pole gas generator prime mover
6,000 RPM (Internal Combustion Engine Redline)	`628.32`	High-revving automotive V6/V8	Automotive peak power dyno operating point
10,000 RPM (EV Traction Motor - High Speed)	`1047.2`	Modern electric vehicle gearbox input	Permanent magnet synchronous EV drivetrain
15,000 RPM (Formula 1 Turbo Power Unit)	`1570.8`	FIA technical regulation limit	Motorsport hybrid MGU-K & ICE maximum revs

Frequently Asked Questions

There are exactly 0.86796166 pound-force inches (lbf·in) in 1 kilogram-force centimeter (kgf·cm). To calculate larger amounts manually, simply multiply your total number of kilogram-force centimeters by the conversion multiplier of 0.86796166.

The mathematical formula to convert kilogram-force centimeters to pound-force inches is: [value] * 0.86796166 = pound-force inches. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from pound-force inches back to kilogram-force centimeters, you must divide your starting value by 0.86796166. Our bidirectional tool automatically computes this inverse equation the moment you type into the pound-force inch input field.

1 Pound-force inch is larger than 1 Kilogram-force centimeter. Specifically, 1 Kilogram-force centimeter equals 0.86796166 pound-force inches, meaning 1 Pound-force inch is 1.1521 times larger than 1 Kilogram-force centimeter (a difference of 0.06 orders of magnitude). Expressing measurements in kilogram-force centimeters requires a larger numerical value to represent the equivalent physical magnitude.

A typical robotics hobby RC digital servo motor stall torque rating measures 15 kgf·cm, which corresponds to 13.0194 lbf·in (Pound-force inch).

There are 0.867962 lbf·in in 1 kgf·cm.

The exact mathematical formula is V(lbf·in) = V(kgf·cm) × 0.867962.

The reverse formula is V(kgf·cm) = V(lbf·in) × 1.15212.

Pound-force inches are typically used in the aerospace and electronics industries for defining torque limits on small fasteners, where lbf·ft would be too coarse of a measurement.

Related Kilogram-force centimeter and Pound-force inch Conversions

Convert Kilogram-force centimeter to Other Units

Kilogram-force centimeter to Newton meter Kilogram-force centimeter to Dyne centimeter Kilogram-force centimeter to Gram-force meter Kilogram-force centimeter to Gram-force centimeter Kilogram-force centimeter to Kilogram-force meter Kilogram-force centimeter to Pound-force foot Kilogram-force centimeter to Ounce-force inch Kilogram-force centimeter to Kilonewton meter

Convert Other Units to Pound-force inch

Newton meter to Pound-force inch Dyne centimeter to Pound-force inch Gram-force meter to Pound-force inch Gram-force centimeter to Pound-force inch Kilogram-force meter to Pound-force inch Pound-force foot to Pound-force inch Ounce-force inch to Pound-force inch Kilonewton meter to Pound-force inch

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