Force conversion family

Force unit conversions

Force is the mechanical quantity represented by mass times acceleration; the newton (N), equal to kg m s^-2, is its coherent SI unit.

Five named units

Unit and factor reference

Base: N

Factors are stored as decimal strings relative to newton (N).
Unit	Symbol	Factor to base	Relationship	Definition and variant
newton	`N`	`1`	defined	The newton is the coherent SI unit of force: 1 N = 1 kg m s^-2. The base factor is exactly 1 by the family base-unit choice.
kilonewton	`kN`	`1000`	exact	A kilonewton is the SI decimal multiple formed by applying kilo (10^3) to newton: 1 kN = 1000 N. The decimal-prefix relationship is exact.
pound-force	`lbf`	`4.4482216152605`	exact	One pound-force is the force associated with one avoirdupois pound under standard acceleration of free fall; the exact reference factor is 4.4482216152605 N. Named variant: Avoirdupois pound-force at standard gravity; not pound mass or poundal. The factor is the exact decimal product 0.45359237 kg × 9.80665 m/s^2 = 4.4482216152605 N.
dyne	`dyn`	`0.00001`	exact	The dyne is the CGS force unit and equals exactly 10^-5 newton. Named variant: CGS force unit; non-SI. The terminating decimal factor is exact.
kilogram-force	`kgf`	`9.80665`	conventional	One kilogram-force is the force associated with one kilogram under standard acceleration of free fall: 1 kgf = 9.80665 N. Named variant: Standard-gravity kilogram-force; obsolete/non-SI and not local weight. The terminating factor follows the conventional exact standard-gravity value 9.80665 m/s^2.

Every ordered pair

All 20 force calculators

From newtons (N)

From kilonewtons (kN)

From pounds-force (lbf)

From dynes (dyn)

From kilogram-force (kgf)

Evidence and review status

This family is machine-reviewed-pending-human. Automated checks verify structure, factor parity and source references; they do not constitute human or specialist approval.

Family assumptions and limits

Signed values preserve a chosen direction; the sign is not a different force unit.
Pound-force is force, not pound mass. Its factor uses the avoirdupois pound and standard acceleration of free fall, not local gravity.
Kilogram-force also uses standard acceleration of free fall and is a non-SI gravitational unit; it is not a kilogram of mass.
NIST generally discourages the non-SI force units in this family; they are retained for conversion compatibility.
A conversion does not add significant figures to the source measurement.

Authoritative references

The International System of Units (SI), 9th edition, version 4.01; Bureau International des Poids et Mesures; Cover (V4.01, June 2026); section 2.3.4, Table 4 on p. 133 defines force/newton/N as kg m s^-2; chapter 3, Table 7 on p. 138 defines kilo; 3rd CGPM declaration reproduced on p. 154 gives standard gravity as 980.665 cm/s^2 and notes kilogram-force is obsolete.; accessed 2026-08-07
NIST Guide to the SI, Appendix B.9: Factors for Units Listed by Kind of Quantity or Field of Science; National Institute of Standards and Technology; Force table: dyne = 1.0 E-05 N, kilogram-force = 9.80665 N, and pound-force = 4.448222 N at displayed precision.; accessed 2026-08-07
NIST Guide to the SI, Footnotes; National Institute of Standards and Technology; Footnotes 22-23: the avoirdupois pound factor is exactly 0.45359237 kg and, using standard free-fall acceleration 9.80665 m/s^2, the exact pound-force factor is 4.4482216152605 N.; accessed 2026-08-07

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