I'm almost certainly missing something here so I'd be grateful if someone could explain but how do I convert thrust in newtons to specific impulse?



You can't directly convert them; they're two different measures. As Organic Marble points out, thrust is loosely analogous to a car's horsepower; specific impulse is loosely analogous to a car's gas mileage.

Thrust in newtons is equal to the propellant mass exhaust flow rate in kg/s times the specific impulse in N·s/kg (which is dimensionally equivalent to m/s), however.

You more often see specific impulse given in seconds; multiply seconds by 9.81 to get N·s/kg. Note that the use of standard gravity as a conversion factor does not mean that specific impulse changes under different gravity. Rather, it's required because of the historical conflation of "pound" as both a unit of force and a unit of mass. Specific impulse in seconds is really "pounds-force seconds per pound-mass" which has the same dimensionality as N·s/kg.


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