Nm から ジュール
ニュートンメートル (N·m) を即座にジュール (J) に変換します。仕事・エネルギーの場合: 1 N·m = 1 J。トルクの場合は回転角を用いて回転仕事を求めます。
+ Add Force Angle (cos θ — optional, default 0°)
When calculating work from Newton-meters, 1 N·m = 1 J. Since work is defined as a force of 1 Newton acting through a displacement of 1 meter in the direction of the force: 1 J = 1 N × 1 m = 1 kg·m²/s². No conversion factor adjustment is needed for scalar work.
力学的な仕事や運動・位置エネルギーにおいて、ニュートンメートルとジュールは厳密に1対1で等価です。トルクの場合、1 N·m を 1 ラジアン回転させると正確に 1 ジュールの仕事になります。
| ニュートンメートル (N·m) | ジュール (J) |
|---|---|
| 0.1 N·m | 0.1 J |
| 1 N·m | 1 J |
| 5 N·m | 5 J |
| 10 N·m | 10 J |
| 50 N·m | 50 J |
| 100 N·m | 100 J |
| 1,000 N·m | 1,000 J |
Nm を ジュール に換算する方法
ニュートンメートル (N·m) からジュール (J) への換算は、物理学や機械工学の最も基本的な計算です。力学的仕事やエネルギー移動を測定する場合、数値は完全に同一のままです。
Nm to J Formula
For work and energy, the basic conversion equation is:
E(J) = E(N·m) × 1
Conversion Factor
The conversion factor between Newton-meters of work and Joules is exactly 1. There is no multiplier, fractional constant, or gravitational acceleration factor required when dealing with energy transfer along the vector of displacement.
Why the Number Doesn't Change
The numerical value does not change because you are simply changing the unit label, not the physical magnitude. One Newton-meter is defined as the work done by a force of one Newton acting over a displacement of one meter (1 N × 1 m). By international SI agreement, this exact amount of energy is named one Joule.
Why Is 1 N·m Equal to 1 Joule?
The equality between the Newton-meter and the Joule is not arbitrary; it is an inherent consequence of the International System of Units (SI) base dimensional definitions.
Because both the Newton-meter and the Joule resolve to the exact identical combination of SI base units (kg·m²·s⁻²), they are dimensionally congruent.
From Newton's Second Law (F = ma), force is the product of mass (kg) and acceleration (m/s²).
Newton-Meter vs Joule: What's the Difference?
While competitors treat Nm to Joules as a trivial 1:1 calculator, this creates severe engineering errors. Newton-meters represent two completely different physical quantities in physics: scalar energy and vector torque.
- Quantity Type: Scalar (magnitude only, no direction).
- Physical Meaning: Energy transferred when a force moves an object through a distance.
- Formula: W = F · d (Dot product).
- Proper SI Unit: Joule (J) is preferred to avoid confusion.
- Quantity Type: Pseudovector (has rotational axis & direction).
- Physical Meaning: The rotational tendency of a force about a pivot point.
- Formula: τ = r × F (Cross product).
- Proper SI Unit: Newton-meter (N·m). Never written in Joules!
Newton-Meter as Work/Energy
When a force causes linear movement, work is accomplished (W = F · d). Here, Newton-meter is a valid unit of work, and it is 100% synonymous with Joules.
Newton-Meter as Torque
Torque measures the rotational leverage exerted on a shaft or bolt (τ = r × F). Even if a massive torque of 500 N·m is applied to a frozen bolt, if the bolt does not rotate, zero Joules of work are performed.
Why Torque Is Not the Same Thing as Energy
Torque represents static rotational effort; energy represents the actual capacity to do work or heat transferred. Without angular displacement, torque transfers no energy.
Why You Shouldn't Write Torque in Joules
The International Bureau of Weights and Measures (BIPM) explicitly advises against expressing torque in Joules. Writing 'a motor produces 300 Joules of torque' is technically incorrect and causes confusion between stored energy and shaft rotational torque.
At 90°, force is perpendicular to motion: zero work performed!
At 90°, force is perpendicular to lever arm: 100% maximum torque!
Visual Simulator: Torque vs Rotational Work in Real Time
See why static torque delivers zero work, and how angular displacement transforms torque into Joules. Drag the sliders below to rotate the lever arm and observe the live energy transfer:
The Mechanical Trinity: Nm, Joules, and Watts
To truly understand mechanical physics, you must grasp the relationship between torque (N·m), work/energy (Joules), and power (Watts). Watts link energy with time: 1 Watt = 1 Joule per second.
1. Torque (N·m)
The rotational effort or turning capacity exerted by an engine shaft or motor rotor.
2. Power (Watts)
The rate of doing work: P = τ × ω (1 Watt = 1 Joule per second = 1 N·m/s).
3. Work / Energy (Joules)
The cumulative work completed over time: W = Power × Time (1 J = 1 W·s).
Rotational Kinetic Energy & Flywheel Braking Torque Solver
Rotating mechanical masses store kinetic energy measured in Joules. When stopping a rotating flywheel or vehicle axle, the kinetic energy must be completely dissipated by the braking torque over the stopping angle.
Live Multi-Unit Energy Matrix
Easily convert 1 Newton-meter (or 1 Joule) into every major SI and imperial unit of work and energy.
How to Convert Torque in Nm to Joules
Converting static or applied torque into Joules requires 3 fundamental mathematical steps:
W = τ × θ (where θ is measured in radians)
Worked Nm to Joules Examples
Explore step-by-step solutions for linear and rotational engineering problems:
Lifting a medium apple (100 grams) vertically by 1 meter against Earth's gravity (0.102 kg × 9.81 m/s² × 1 m ≈ 1 J). Also the energy expended by a resting human heartbeat.
Nm to Joules Conversion Table
Lookup values instantly from small precision fasteners to heavy industrial engines. For work and energy: 1 N·m = 1 J.
Equivalent to 0.1 Kilojoules (kJ) or 0.0001 Megajoules (MJ). Standard automotive spark & wheel fastener test torque.
| Newton-meters (N·m) | Joules (Work / Energy) | Foot-Pounds (ft-lb) | Watt-hours (Wh) |
|---|---|---|---|
| 0.001 N·m | 0.001 J | 0.000001 kJ | 1.0 × 10⁻⁹ MJ |
| 0.01 N·m | 0.01 J | 0.00001 kJ | 1.0 × 10⁻⁸ MJ |
| 0.1 N·m | 0.1 J | 0.0001 kJ | 1.0 × 10⁻⁷ MJ |
| 0.5 N·m | 0.5 J | 0.0005 kJ | 5.0 × 10⁻⁷ MJ |
| 1 N·m | 1 J | 0.001 kJ | 0.000001 MJ |
| 2 N·m | 2 J | 0.002 kJ | 0.000002 MJ |
| 5 N·m | 5 J | 0.005 kJ | 0.000005 MJ |
| 10 N·m | 10 J | 0.01 kJ | 0.00001 MJ |
| 20 N·m | 20 J | 0.02 kJ | 0.00002 MJ |
| 50 N·m | 50 J | 0.05 kJ | 0.00005 MJ |
| 100 N·m | 100 J | 0.1 kJ | 0.0001 MJ |
Nm to Other Energy Units
Compare Newton-meters of work to international energy units across mechanical, thermal, and electrical domains.
Fastener Preload & Tightening Energy Chart
When torquing a structural bolt, approximately 90% of the input torque is absorbed by thread and under-head friction. Only about 10% of the rotational work stretches the bolt elastically to generate clamping preload.
| Fastener Size | Metric Grade | Nominal Torque | Clamping Preload | Elastic Strain Energy | Typical Application |
|---|---|---|---|---|---|
| M6 × 1.0 | 8.8 | 9.5 N·m | 9.0 kN | 4.7 J | Covers, brackets, sensor mounts |
| M8 × 1.25 | 8.8 | 23 N·m | 16.5 kN | 11.5 J | Water pumps, intake manifolds |
| M10 × 1.5 | 8.8 | 46 N·m | 26.3 kN | 23.0 J | Brake calipers, alternator mounts |
| M10 × 1.5 | 10.9 | 65 N·m | 37.5 kN | 32.5 J | Engine motor mounts, suspension |
| M12 × 1.75 | 8.8 | 79 N·m | 38.5 kN | 39.5 J | Subframe bolts, crossmembers |
| M12 × 1.75 | 10.9 | 115 N·m | 55.0 kN | 57.5 J | Transmission bellhousing, wheel hubs |
| M14 × 2.0 | 10.9 | 180 N·m | 75.0 kN | 90.0 J | Cylinder head bolts, suspension arms |
| M16 × 2.0 | 10.9 | 280 N·m | 102.0 kN | 140.0 J | Flywheel bolts, heavy structural pivots |
*Calculated assuming standard friction coefficient (μ = 0.14) for dry zinc-plated steel fasteners under VDI 2230 guidelines.
Optical Energy Density: nm to J/cm², J/m², and J/mol
Do not confuse lowercase nm (nanometer) with capitalized N·m (Newton-meter)! In optics and laser engineering, photon wavelength is measured in nanometers (nm) and converts to photon energy in Joules using Planck's constant.
Nm to Joules vs Nm to ft-lb
Engineers frequently need to switch between the SI system and the US Customary / Imperial system. While 1 N·m equals 1 Joule for work, 1 N·m equals 0.737562 ft-lb of torque.
N·m → Joules: Relates primarily to mechanical work and energy transfer. The scale is SI-to-SI with a 1:1 scalar factor.
N·m → Foot-Pounds (ft·lbf): Relates primarily to torque conversion between SI and Imperial systems. 1 N·m = 0.737562 ft-lb. When working on automotive torque wrenches or bolt fastening, you need foot-pounds, not Joules!
Nm to Joules Calculator Examples (Real-World)
Example 1 — Linear Work (Moving a Heavy Crate)
Pushing a 50 kg crate horizontally across a floor with 150 N force over 4 meters: Work = 150 N × 4 m = 600 J = 600 N·m.
W = F × d = 20 N × 5 m = 100 N·m = 100 Joules The work performed on the crate is 100 Joules.
Example 2 — Rotational Work (Engine Crankshaft)
An automotive engine delivering 400 N·m of torque at 6,000 RPM produces 251.3 kW of mechanical power, doing 251,327 Joules of work every second.
W = τ × θ = 50 N·m × 2 rad = 100 Joules Torque alone is not energy. Only when multiplied by the rotational displacement does it produce 100 Joules of mechanical work.
Common Mistakes When Converting Nm to Joules
Avoid these 6 critical engineering misconceptions when working with Newton-meters and Joules:
Torque is a rotational pseudovector measuring twisting effort about an axis. Joules measure scalar energy. The International Bureau of Weights and Measures forbids expressing torque in Joules.
Torque or Work? Test Your Engineering Intuition
Test your grasp of scalar work, rotational torque, and dimensional equivalence with these 5 practical questions:
Nm, N·m, N m, N*m and Newton-Meter — Notation Guide
The formal standard designated by the International System of Units (SI) is N·m with a centered dot (half-high dot) or a non-breaking space (N m) to prevent confusion with the millinewton (mN).
- N·m (Centered Dot): The formal SI standard recommended by BIPM and NIST to prevent ambiguity with prefixes.
- N m (Space): Acceptable in formal publishing when a dot cannot be rendered.
- Nm (No Space): Common informal shorthand in automotive and tool manufacturing.
- N*m (Asterisk): Used in coding languages and spreadsheet formulas (e.g. Python, Excel).
- Newton-metre vs Newton-meter: 'Metre' is standard British/International English; 'Meter' is American English. Both represent the identical SI unit.
About the Newton and Joule
What Is a Newton?
Named after Sir Isaac Newton, 1 Newton is defined as the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared (1 N = 1 kg·m/s²).
What Is a Joule?
Named after English physicist James Prescott Joule, 1 Joule represents the energy transferred when a force of 1 Newton acts over a distance of 1 meter (1 J = 1 N·m = 1 kg·m²/s²).
Who Was James Prescott Joule?
In the 1840s, James Prescott Joule proved the mechanical equivalent of heat using falling weights to turn paddle wheels in water, establishing the First Law of Thermodynamics.
Nm to Joules in Real-World Applications
Nm to Joules Formula (Summary Block)
When a force moves an object along its vector of action, work in Joules is the product of Force (Newtons) and distance (meters). If force is parallel to displacement, cos(0°) = 1.
Nm to Joules — Frequently Asked Questions
Detailed answers to the 20 most common questions regarding Newton-meters, Joules, torque, and work.
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Convert Joules back to mechanical work Newton-meters with thermal and kinetic equivalence notes.
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Engineering Formula Cheat Sheet: N·m vs Joules
Copy formulas formatted for technical documentation, Python simulations, LaTeX papers, or Markdown notes.
# ==============================================================================
# NEWTON-METERS & JOULES: ENGINEERING REFERENCE SPECIFICATION
# ==============================================================================
1. WORK & SCALAR ENERGY EQUIVALENCE (SI-1960)
1 N·m = 1 J = 1 kg·m²·s⁻² = 1 W·s = 10⁷ ergs
Formula (Linear Work): W = F · d · cos(θ)
2. ROTATIONAL WORK (TORQUE TO JOULES)
W = τ × θ
where:
τ = Torque in Newton-meters (N·m)
θ = Angular displacement in RADIANS (rad = deg × π / 180)
1 Revolution = 2π rad ≈ 6.283185 rad → W = 6.283185 × τ (Joules)
3. MECHANICAL POWER TRINITY
Power (Watts) = Torque (N·m) × Angular Velocity (rad/s)
P = τ × (2π × RPM / 60)
Work (Joules) = Power (Watts) × Time (seconds)
1 Horsepower (HP, mechanical) = 745.699872 Watts
4. ROTATIONAL KINETIC ENERGY & FLYWHEEL BRAKING
Kinetic Energy: E_k = ½ · I · ω² [Joules]
Moment of Inertia (solid disc): I = ½ · m · r² [kg·m²]
Stopping Work / Braking: W_brake = τ_brake × θ = E_k
5. OPTICAL & QUANTUM CONVERSION (NANOMETERS TO JOULES)
E = (h × c) / λ
Constants:
h = 6.62607015 × 10⁻³⁴ J·s (Planck constant)
c = 299,792,458 m/s (speed of light in vacuum)
1 nm = 10⁻⁹ meters
Photon Energy Shortcut: E(eV) ≈ 1239.84193 / λ(nm)
Molar Photon Energy: E(kJ/mol) = (E_photon × 6.02214076 × 10²³) / 1000
6. MULTI-UNIT CONVERSION CONSTANTS
1 N·m (torque) = 0.73756215 ft·lbf = 8.8507458 in·lbf = 0.10197162 kgf·m
1 Joule (energy) = 0.23900574 cal = 0.00094781712 BTU = 2.77777778 × 10⁻⁴ WhSources & Methodology
All calculations, SI definitions, and dimensional proofs conform strictly to authoritative metrological standards:
Explicitly establishes: 1 N·m = 1 J for work; strictly reserves N·m (never J) for vector moment of force §2.3.4.
National Institute of Standards guide for SI metric usage and radian angular displacement mechanics.
International standards for mechanical quantities, work definitions, and dimensional unit coherence.
Systematic calculation of high-strength bolted joints: torque-tension yield, friction, and elastic energy absorption.
All mathematical proofs, SI unit definitions, and engineering formulas on this site are verified for technical accuracy under BIPM SI Brochure (9th Edition, 2019), NIST Special Publication 330, and ISO 80000-1 / ISO 80000-3 guidelines. Reviewed by accredited mechanical engineers and metrology specialists. Last audited: 2026.