# Is there a relatively painless way to calculate the radius of a neutron star, given its mass?

I know there are different models based on, as I understand it, different equations of state describing the neutron star mass-raduis relation. I'm not sure what to do with that, though.

My math isn't particulary strong. I was hoping for something as inviting as E=mc², but I'm willing to settle for something slightly more intimidating than the Schwarzchild radius equation.

• Sorta what the TOV equation is for, I think. Though not really "painless", I should think. – Kyle Kanos Apr 13 at 0:20
• @KyleKanos My understanding is that the TOV limit puts an upper bound on the mass of a neutron star, but says nothing of one's radius. I'll have to take a harder look at the equation. So far, I'm not seeing where a value for radius falls out of it. – user213717 Apr 13 at 0:46
• Related, possible duplicate physics.stackexchange.com/q/264995 – PM 2Ring Apr 13 at 5:30
• @PM2Ring Thanks. That's interesting, but it's not what I was asking for. If I know the Black Widow Pulsar has a high end mass estimate of around 2.4 solar masses, probably right on the edge of the TOV limit, is there an equation, based on a model of a neutron star's mass-radius relation, I can plug that into that will give me that particular star's radius? – user213717 Apr 13 at 6:46
• No there isn't a painless way. Assuming it is 10km is almost as good as the accuracy we can identify for any particular model. – Rob Jeffries Apr 13 at 8:14