Toolarithm

Unit Converter

Torque Converter

Exact torque. Clear moment arms.

Convert a torque

Exact units. Clear moment arms.

Signed decimal, scientific value, fraction or mixed number; sign follows your declared moment sense.

Optional force at a moment arm

The main result remains torque. The separate force calculation does not infer tool geometry, fastener preload or allowable loads.

View torque results
Precision and report

Decimal/scientific input supports twenty significant digits, eighty characters and written exponents from negative thirty through thirty. Fractions support one hundred digits per component and two hundred forty characters per field. Display digits do not add measurement accuracy.

Worked examples

Torque in newton-meters

τt≈135.581794833 N m\tau_t\approx135.581794833\,\mathrm N\,\mathrm{m}

Exact force and length definitions; only displayed values are rounded. This is torque or moment of force, not work or energy.

Torque conversion record

Entered torque

τs=100.000000000 lbf ft\tau_s=100.000000000\,\mathrm{lbf}\,\mathrm{ft}

Normalized moment

τSI≈135.581794833 N m\tau_{\mathrm{SI}}\approx135.581794833\,\mathrm N\,\mathrm m

Source-to-target multiplier

k≈1.35581794833k\approx1.35581794833

Each row describes the same torque. A foot and an inch are different lengths; pounds here mean pound-force. Kilogram-force units retain defined standard gravity. Newton-meters are kept distinct from joules as a quantity label.

Torque in every supported unit

All twenty-five rows describe the total torque. Complete text and CSV retain every row even when this table is hidden.

The same moment of force in twenty-five named torque units
Unit conventionConverted torque
Newton-meters135.581794833 N m135.581794833\,\mathrm N\,\mathrm{m}
Pound-force feet100.000000000 lbf ft100.000000000\,\mathrm{lbf}\,\mathrm{ft}
Pound-force inches1200.00000000 lbf in1200.00000000\,\mathrm{lbf}\,\mathrm{in}
Kilogram-force meters13.8254954376 kgf m13.8254954376\,\mathrm{kgf}\,\mathrm{m}
Kilogram-force centimeters1382.54954376 kgf cm1382.54954376\,\mathrm{kgf}\,\mathrm{cm}
Dyne centimeters1.35581794833×109 dyn cm1.35581794833\times10^{9}\,\mathrm{dyn}\,\mathrm{cm}
Newton-centimeters13558.1794833 N cm13558.1794833\,\mathrm N\,\mathrm{cm}
Newton-millimeters135581.794833 N mm135581.794833\,\mathrm N\,\mathrm{mm}
Kilonewton-meters0.135581794833 kN m0.135581794833\,\mathrm{kN}\,\mathrm{m}
Meganewton-meters (capital M)0.000135581794833 MN m0.000135581794833\,\mathrm{MN}\,\mathrm{m}
Millinewton-meters (lowercase m)135581.794833 mN m135581.794833\,\mathrm{mN}\,\mathrm{m}
Micronewton-meters1.35581794833×108 μN m1.35581794833\times10^{8}\,\mathrm{\mu N}\,\mathrm{m}
Kilogram-force millimeters13825.4954376 kgf mm13825.4954376\,\mathrm{kgf}\,\mathrm{mm}
Gram-force centimeters1382549.54376 gf cm1382549.54376\,\mathrm{gf}\,\mathrm{cm}
Gram-force millimeters1.38254954376×107 gf mm1.38254954376\times10^{7}\,\mathrm{gf}\,\mathrm{mm}
Gram-force meters13825.4954376 gf m13825.4954376\,\mathrm{gf}\,\mathrm{m}
Ounce-force inches19200.0000000 ozf in19200.0000000\,\mathrm{ozf}\,\mathrm{in}
Ounce-force feet1600.00000000 ozf ft1600.00000000\,\mathrm{ozf}\,\mathrm{ft}
Kip-feet (kip times international foot)0.100000000000 kip ft0.100000000000\,\mathrm{kip}\,\mathrm{ft}
Kip-inches (kip times international inch)1.20000000000 kip in1.20000000000\,\mathrm{kip}\,\mathrm{in}
Poundal feet3217.40485564 pdl ft3217.40485564\,\mathrm{pdl}\,\mathrm{ft}
Poundal inches38608.8582677 pdl in38608.8582677\,\mathrm{pdl}\,\mathrm{in}
Dyne meters1.35581794833×107 dyn m1.35581794833\times10^{7}\,\mathrm{dyn}\,\mathrm{m}
Dyne millimeters1.35581794833×1010 dyn mm1.35581794833\times10^{10}\,\mathrm{dyn}\,\mathrm{mm}
Metric tonne-force meters0.0138254954376 tfmetric m0.0138254954376\,\mathrm{tf}_{\mathrm{metric}}\,\mathrm{m}

Step-by-step torque conversion

  1. 1. Normalize the named torque unit

    Multiply its exact force factor by its exact length factor. A signed scalar moment retains your declared moment sense; this does not calculate a vector cross product from coordinates.

    τSI=τsfs≈135.581794833 N m\tau_{\mathrm{SI}}=\tau_s f_s\approx135.581794833\,\mathrm N\,\mathrm m

  2. 2. Divide by the exact destination torque factor

    Convert the unrounded newton-meter quantity into the selected torque convention. The approximation mark refers to display rounding; no force, lever geometry or energy is inferred from changing units.

    τt=τSIft≈135.581794833 N m\tau_t=\frac{\tau_{\mathrm{SI}}}{f_t}\approx135.581794833\,\mathrm N\,\mathrm{m}
What Can You Create?

Compare torque conventions and inspect perpendicular moments

Convert a stated moment of force

Translate between named metric, customary, gravitational and CGS torque conventions. All six original unit identifiers remain available, with pound-force feet and pound-force inches clearly distinguished.

Model force at a perpendicular arm

Choose the signed force and nonnegative perpendicular moment arm independently. Both are normalized before multiplication, preserving the declared scalar moment sense without guessing a force angle.

Resolve force at another stated arm

Keep the converted torque unchanged while calculating the force associated with a separately supplied positive perpendicular arm. A zero arm produces an explicit undetermined-force notice instead of a finite answer.

Torque conversion formulas and worked examples

Multiply force and length factors

A named torque unit combines a force unit and a length unit. Let fFf_F be newtons per force unit and fLf_L be meters per length unit. Their product is the torque factor into newton-meters. Converting to another torque convention then divides by that target factor. This changes a unit representation while preserving the scalar sign and the original physical interpretation of the stated moment.

fτ=fFfL,τSI=τsfs,τt=τsfsftf_{\tau}=f_Ff_L,\qquad \tau_{\mathrm{SI}}=\tau_s f_s,\qquad \tau_t=\tau_s\frac{f_s}{f_t}

Example: the original pound-force-foot conversion

The pound-force factor is exactly 4.4482216152605 N4.4482216152605\,\mathrm N per pound-force, and the international foot is exactly 0.3048 m0.3048\,\mathrm m. Their product gives the exact torque relationship. Applying it to the original hundred-pound-force-foot input yields an unrounded rational result before display precision is selected. A smaller inch-based length uses a different torque factor even though its force unit has the same name.

1 lbf ft=1.3558179483314004 N m,100 lbf ft=135.58179483314004 N m1\,\mathrm{lbf}\,\mathrm{ft}=1.3558179483314004\,\mathrm N\,\mathrm m,\qquad 100\,\mathrm{lbf}\,\mathrm{ft}=135.58179483314004\,\mathrm N\,\mathrm m

Example: force and perpendicular moment arm

For a stated force of 200 N200\,\mathrm N and a perpendicular moment arm of 0.5 m0.5\,\mathrm m, the scalar moment is 100 N m100\,\mathrm N\,\mathrm m in the declared moment sense. Reversing that sense makes the signed force and resulting torque negative while the perpendicular distance remains nonnegative. The distance must already represent the required geometry; a slanted lever's full length cannot be substituted without checking its relationship to the force line of action.

τ=Fd⊥=(200 N)(0.5 m)=100 N m\tau=Fd_{\perp}=(200\,\mathrm N)(0.5\,\mathrm m)=100\,\mathrm N\,\mathrm m

Example: resolving force without changing torque

The same stated torque of 100 N m100\,\mathrm N\,\mathrm m at a separately supplied perpendicular arm of 0.5 m0.5\,\mathrm m resolves to 200 N200\,\mathrm N. This is a separate force quantity rather than another torque unit. A positive arm is needed for a determined finite result. The calculation alone does not supply wrench-extension geometry, friction, bolt preload or an allowable force, so those physical inputs remain distinct from the numerical relationship being checked.

Freq=τd⊥,req=100 N m0.5 m=200 NF_{\mathrm{req}}=\frac{\tau}{d_{\perp,\mathrm{req}}}=\frac{100\,\mathrm N\,\mathrm m}{0.5\,\mathrm m}=200\,\mathrm N
Why Users Love This Tool

Trace exact force and length definitions before rounding

Conventions remain explicit

  • Exact torque factors are products of named force and length factors.
  • Full labels distinguish force from mass, feet from inches and SI prefix capitalization.
  • Torque stays a moment-of-force quantity and is not relabeled as work or energy.

Geometry and precision travel with the result

  • Normalized force and perpendicular arm remain visible for derived moments.
  • Lossless swaps and exact numerical certificates avoid rounded-source drift.
  • Complete CSV, accessible mathematics, validated sharing and guarded printing keep a reviewable record across devices.
Perfect For

Useful for mechanics, specifications and unit-review work

Technical specification review

Check whether two torque figures use the same force and length conventions before comparing them. Explicit labels prevent a foot-based moment from being mistaken for an inch-based moment or a mass-based shorthand.

Mechanics and geometry exercises

Apply an already established perpendicular moment arm and a declared moment sense. Inspect zero-arm boundaries and separate force resolution without assuming a full lever length or an unstated angle.

Students and mathematical documentation

Follow exact factor products, compare related torque units, and distinguish a moment of force from energy. Copy properly delimited LaTeX steps or retain a complete numerical CSV for later checking.

How It Works

How it works in three quick steps.

1

State the torque or perpendicular moment model

Choose a signed torque value or a signed force with a nonnegative perpendicular moment arm. Enter complete values and select each force, length or torque convention explicitly.

2

Choose the destination and inspect geometry

Select the target torque unit and significant figures. Optionally supply a separate perpendicular moment arm to resolve the required force. Review the normalized torque, model inputs and calculation steps.

3

Save the result with its moment convention

Copy complete text or LaTeX working, download all unit rows and numerical certificates as CSV, share validated active settings or print the selected visible report to PDF. Retain moment sense and geometry assumptions with the record.

Download & Print

Save the torque convention and moment-arm assumptions together

Copy a full record or LaTeX steps

Copy the complete plain-text calculation or display-delimited mathematical working. A versioned share link restores active torque or moment-model inputs, required-force settings and report preferences after validation.

Download every torque row as CSV

The quoted UTF-8 file retains all twenty-five torque conventions, exact numerical certificates, model geometry, required-force context and calculation steps. Hidden report sections remain in the complete saved record.

Print or save the visible report

Use the browser’s PDF destination after reviewing page size and scale. Hide the full unit table for a compact report when appropriate. Extremely long exact fractions retain all digits in text and CSV rather than spilling outside a readable printed page.

FAQ

Frequently Asked Questions

How do I convert pound-force feet to newton-meters?
Multiply the torque by the exact factor 1.3558179483314004 N m/(lbf ft)1.3558179483314004\,\mathrm{N\,m/(lbf\,ft)}. That factor is the product of the defined pound-force and international-foot factors. The original example uses one hundred pound-force feet. An inch-based torque label has a different length factor, so pound-force inches must not be treated as pound-force feet. The converter names both conventions and retains exact numerical arithmetic before applying the selected display significant figures.
Are foot-pounds and inch-pounds the same torque?
No. In this torque context the pound means pound-force, and the length convention still matters. Because one international foot contains twelve international inches, 1 lbf ft=12 lbf in1\,\mathrm{lbf\,ft}=12\,\mathrm{lbf\,in}. A bare pound label can also hide confusion between mass and force, so this page uses the full force-unit names in the menus and records. Confirm the intended torque convention in the source specification before choosing a unit; magnitude alone cannot resolve an ambiguous label.
Is a newton-meter of torque the same quantity as a joule of energy?
Torque and energy share physical dimensions but are different quantities. Torque is expressed here in newton-meters rather than relabeled as joules. Mechanical work during a rotation additionally depends on angular displacement; for a constant aligned torque, W=τθW=\tau\theta with angle in radians. A unit conversion of torque alone does not supply that rotation or determine the work performed. The result table therefore contains torque conventions and deliberately does not offer energy units as interchangeable outputs.
Which lever-arm distance should I enter?
Enter the nonnegative perpendicular distance from the selected axis to the force line of action. It is not automatically the full length of a tilted lever or wrench. In a planar geometry with the usual angle between the position and force vectors, the magnitude relationship is ∣τ∣=r∣F∣sin⁡θ|\tau|=r|F|\sin\theta, and the perpendicular moment arm accounts for that geometry. This tool expects that perpendicular distance directly rather than silently assuming a force angle or calculating a vector cross product from unspecified coordinates.
Can torque or the force in the moment model be negative?
Yes. The converter accepts signed scalar torques and signed model forces, with the sign referring to a moment sense you declare. Positive and negative signs are not universal clockwise or counterclockwise labels without a chosen axis and viewing convention. The moment-arm distance itself remains nonnegative. Multiplying it by the signed model force preserves the declared moment sense, and changing torque units preserves that sign. The page does not rotate axes, combine multiple vector moments or infer three-dimensional geometry.
What happens when the perpendicular moment arm is zero?
In the forward model, a finite force with zero perpendicular arm produces zero modeled moment through τ=Fd⊥\tau=Fd_{\perp}. In the separate force-resolution section, dividing a nonzero torque by a zero arm cannot produce a finite force. Zero torque with zero arm also leaves the force undetermined. The tool keeps the main torque conversion valid and explains that boundary instead of displaying an arbitrary force. A positive required-force arm and zero torque, by contrast, resolve to zero force.
Can this calculate a safe wrench setting, bolt preload or extension correction?
The converter changes named torque units and evaluates the explicitly stated perpendicular-arm relationships. It does not infer a manufacturer torque specification, fastener friction, bolt preload, tool calibration, allowable load or the geometry of an offset extension. The optional force output uses its separately stated perpendicular arm and declared moment sense. Retain the actual tool configuration and authoritative specification in your working record; a numerically correct unit conversion alone does not establish those additional physical inputs.
Are all displayed digits exact, and what do saved records retain?
Defined force and length factors and the entered numerical model use exact rational arithmetic. Display significant figures only affect presentation, with approximation marks where rounding changes a value. That arithmetic precision does not improve a torque measurement or wrench calibration. Complete text and CSV preserve every torque row, exact numerator and denominator certificates, active moment-arm inputs, force-resolution context and hidden working. Shared links restore canonical validated settings, while PDF follows visible report preferences and keeps extremely long exact ratios in complete exports rather than overflowing a printed page.
About This Tool

About this Torque Converter

The Toolarithm Torque Converter represents a stated moment of force in another explicitly named torque convention. It preserves the original hundred-pound-force-foot example and its newton-meter destination, together with all six original unit identifiers. Additional metric, customary, gravitational and CGS choices retain their force and length definitions. The product of those exact factors supplies the torque factor, so a rounded numerical shortcut is not mistaken for the complete relationship between units.

Direct input starts from a signed scalar torque whose moment sense is supplied by the user. The alternative moment model starts from a signed force and a nonnegative perpendicular distance from the axis to that force line of action. The force and distance can use independently selected reviewed unit conventions. This model deliberately requires the perpendicular arm instead of treating the full length of a lever as automatically suitable or assuming an unstated force angle. It does not construct vectors or infer a three-dimensional cross product.

A separate optional force-resolution section applies the same total torque at another stated perpendicular arm. This is useful for checking the numerical relationship between moment, force and distance without changing the converted torque. A zero arm cannot determine the force, and that boundary is recorded explicitly while the original unit conversion remains valid. The tool does not infer a calibrated wrench setting, extension correction, fastener friction, bolt preload, structural capacity or allowable load. Those require their own physical context and authoritative specifications.

Exact rational arithmetic preserves the entered numerical model through factor products, moment calculations and force resolution. Display significant figures affect presentation only; exact-result swapping and numerical certificates retain the unrounded arithmetic. Complete text and CSV keep every torque row, active geometry and generated working, including sections hidden from the visible report. Accessible LaTeX and server-rendered defaults support inspection before interactive code loads, while printed reports follow selected visibility preferences. Throughout the page, torque remains a moment-of-force quantity rather than being relabeled as energy merely because the dimensional units can be related.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Conversion factors are normalized to canonical units and checked in both directions. Exact definitions and offset formulas are preferred over rounded lookup values.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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