# How do I get Specific impulse in (s) from (N * s/kg)?

Gross mass        19.32 tonnes
Thrust            1,260 kN
Specific impulse  2314 N·s/kg


How do I get Specific impulse in (s) ?

How do I get Specific impulse in (s)?

First let's look at the units. Always look at the units first.

Specific impulse  2314 N·s/kg


A Newton has units of kg m / s^2, so that is kg m s / s^2 kg which is m/s, and 2314 m/s is a reasonable value for an effective exhaust velocity.

According to the Wikipedia subsection Specific impulse as a speed (effective exhaust velocity) the relationship is:

$$v_e = g_0 \ I_{SP},$$

so flip that around to get:

$$I_{SP} = v_e \ / \ g_0.$$

Since $g_0$ (a standard value for the acceleration due to gravity on Earth) has units of m/s^2, you are dividing m/s by m/s^2 and getting seconds.

The value for $g_0$ in the Wikipedia article is 9.80665 m/s^2, so the $I_{SP}$ is 235.96 sec.

Terminology:

According to the Wikipedia article Specific impulse:

If mass (kilogram or slug) is used as the unit of propellant, then specific impulse has units of velocity. If weight (newton or pound) is used instead, then specific impulse has units of time (seconds).

So $I_{SP}$ in seconds is called weight specific impulse, and when expressed as a velocity, it's called mass specific impulse. See also this answer

• I guess my title is wrong, I'll update it. – Justin808 Feb 15 '18 at 5:53
• @Justin808 It might have been pretty much right in fact. – uhoh Feb 15 '18 at 5:57
• You say "According to the Wikipedia article...", but then link to another SFF answer, also you forgot the underscore in the first link under Terminology – Edlothiad Feb 15 '18 at 8:33
• I obviously mean SX answer not SFF :/ – Edlothiad Feb 15 '18 at 15:14
• @Edlothiad Geoff once unofficially named it SXSE – uhoh Feb 15 '18 at 15:14