Force Conversion Calculator — N, kgf, lbf and dyn

Background.

A luggage scale reads in kilograms, the load cell on a test rig reads in kilonewtons, an American datasheet quotes pound-force, and an old physics textbook works in dynes or poundals. Every one of them is describing a push or a pull, and every one can be written exactly in newtons. That is how this conversion runs: the force you enter is turned into newtons using its unit's defining value, then divided by the defining value of each of the other units, so all seven figures always agree with one another.

None of the factors involved is a measurement. A kilogram-force is the pull of standard gravity, fixed at 9.80665 m/s², on one kilogram, so it is exactly 9.80665 N. A pound-force applies the same idea to the international pound of 0.45359237 kg and comes to exactly 4.4482216152605 N; an ounce-force is a sixteenth of that. A dyne, from the old centimetre-gram-second system, is 10⁻⁵ N. The poundal accelerates one pound of mass by one foot per second squared, which makes it exactly 0.138254954376 N, roughly a thirty-second of a pound-force.

When force conversions go wrong, the arithmetic is rarely to blame. The trouble is the words. "Pound" can mean a mass, a pound-force or, in older British texts, a poundal. "Kilogram" gets used for a mass and for the force a spring balance reads. A gas strut stamped "100 lb", a winch rated at "2,000 lbs" and a hand dynamometer reading "35 kg" are all reporting forces in gravitational units, and they belong in the lbf and kgf boxes, not in a mass converter.

A few anchors are worth carrying in your head. One kilonewton is about 102 kgf or 225 lbf, roughly the weight of a large adult. One kilogram-force is about 9.81 N or 2.2 lbf. One pound-force is about 4.45 N. Anything far from those ratios usually means a unit was misread.

What is force conversion calculator?

Force is the push or pull that changes an object's motion, measured by the mass it would accelerate and how quickly. The SI unit, the newton, is the force that gives one kilogram an acceleration of one metre per second squared, so 1 N = 1 kg·m/s². The seven units offered here fall into two families. Absolute units are built from mass, length and time alone: the newton and kilonewton in SI, the dyne in the centimetre-gram-second system, and the poundal in the foot-pound-second system. Gravitational units are defined as the weight of a standard mass under standard gravity: the kilogram-force, the pound-force and the ounce-force. Because standard gravity is a fixed number rather than the local pull of the Earth, a gravitational unit is just as exact as an absolute one; it simply carries the factor 9.80665 inside it.

Each unit has kept a home. Kilonewtons are the working unit for structural loads, anchor and bolt capacities, and the breaking strengths stamped on climbing carabiners and slings. Aircraft engine thrust is quoted in kilonewtons in Europe and in pound-force in the United States. Kilogram-force lingers on hand dynamometers, hoists and older European machinery, while ounce-force turns up in US specifications for light springs and small mechanisms.

How to use this calculator.

1. 01Type the force into the Force box. A negative value is fine when it stands for direction, for example compression written as negative under a tension-positive convention; the sign carries through to every result.
2. 02Set From unit to the unit the source actually means. A spring, strut, winch or load rating written in "lb" or "kg" is almost always lbf or kgf. If the number really is a mass, multiply it by gravity first or enter it as kgf or lbf, which does that for you at standard gravity.
3. 03Choose the To unit. The converted force appears first, and the same force is listed underneath in all seven units, which saves time when a drawing or specification has to carry both SI and US customary values.
4. 04Glance at the newton figure as a cross-check against the rough anchors: 1 lbf is about 4.45 N, 1 kgf about 9.81 N.
5. 05For very small forces, convert into a small unit such as the dyne or the newton. Results are carried to ten decimal places, so a fraction of a dyne expressed in kilonewtons can come out as 0.
6. 06For a unit missing from the menus, scale one that is there: a kip is exactly 1,000 lbf, a short ton-force 2,000 lbf, a tonne-force 1,000 kgf, a gram-force 0.001 kgf, a meganewton 1,000 kN and a centinewton 0.01 N. A 45 gf switch spring, for instance, is 0.045 kgf, which converts to 0.4413 N.

The formula.

Each unit has one number attached to it: how many newtons it contains. To convert, multiply by the source unit's number and divide by the target's: result = value × (newtons per source unit) ÷ (newtons per target unit). The seven numbers are 1 for the newton, 1,000 for the kilonewton, 0.00001 for the dyne, 9.80665 for the kilogram-force, 4.4482216152605 for the pound-force, 0.27801385095378125 for the ounce-force and 0.138254954376 for the poundal.

Every one of these is exact, and each can be rebuilt from definitions. The kilogram-force is 1 kg × 9.80665 m/s², the standard acceleration of gravity adopted by the General Conference on Weights and Measures in 1901. The pound-force is 0.45359237 kg × 9.80665 m/s², using the international pound fixed in 1959. The ounce-force is that product divided by 16. The poundal is 0.45359237 kg × 0.3048 m/s², the international pound pushed by one international foot per second squared. The dyne is 1 g × 1 cm/s² = 10⁻³ kg × 10⁻² m/s².

Two ratios fall out of those definitions and explain most of the surprises. Pound-force divided by poundal is 9.80665 ÷ 0.3048 = 32.174, which is standard gravity expressed in feet per second squared. Kilogram-force divided by pound-force is 1 ÷ 0.45359237 = 2.2046, the familiar number of pounds in a kilogram, because the same gravity sits inside both units and cancels.

Going through newtons, rather than chaining rounded pairwise factors such as "1 kgf ≈ 2.2 lbf", means the conversion is equally exact in every direction. The only rounding is the final one: results are kept to ten decimal places, which is far finer than any instrument that measures force.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B.3 supplies force conversions for dyne, kilogram-force, pound-force and poundal.
2. [2]BIPM SI Brochure defines the newton and records the standard acceleration convention.
3. [3]NIST SP 330 independently lists newton as kg·m·s⁻².
4. [4]NIST Handbook 44 Appendix C provides customary/SI legal-metrology relationships.
5. [5]NIST CODATA standard gravity page confirms 9.80665 m/s² exactly.