One newton is 0.2248089431 pounds-force. The pound-force is the weight of one pound of mass under standard gravity — which means it is a force, not a mass, and the distinction is the whole reason this page needs care.
About the units
The newton is the SI unit of force, defined as the force that accelerates one kilogram at one metre per second squared. It is named after Isaac Newton and follows directly from his second law. The pound-force belongs to a different tradition: it is defined as the gravitational force on one pound of mass at standard gravity, fixed by international agreement at exactly 9.80665 m/s². That definition makes the pound-force exactly 4.4482216152605 newtons, with no measurement involved — but it also ties the unit to an assumed gravity that does not exist anywhere in particular.
The exact factor
The exact value is 1 lbf = 4.4482216152605 N, from 0.45359237 kg times 9.80665 m/s². Inverted, one newton is 0.22480894309971 lbf. The confusion to guard against is between pound-force and pound-mass, which share a name in ordinary English. On Earth a one-pound object weighs one pound-force, which is why the distinction seems pedantic — until a calculation involves acceleration, in which case the imperial system requires either the slug as a mass unit or a conversion constant of 32.174 dropped into the equation.
Where you meet this conversion
Structural and mechanical engineering wherever American and metric specifications meet. Bolt preload, spring rates, cable tension and actuator output are all quoted in pounds-force in American documentation and newtons in metric. Load cells and force gauges are sold with switchable units for exactly this reason. Rocket and jet engine thrust is given in pounds-force in American sources and kilonewtons elsewhere, which is why the same engine appears with wildly different numbers depending on where you read about it.