# What is the Critical Mass at Which a Star Becomes a Black Hole?

-- | February 21, 2014

Question:  How do you calculate the critical mass for a star to become a black hole? I’m an undergraduate Math major, and this is my senior thesis and I really have no idea where to start.  — Lauren

Answer:  An earlier post to this blog on “Properties of Stars which Result in Black Holes” provides a general overview to this question.  Since the exact mass of an object like a star that must ultimately become a black hole is a function of its radius, there isn’t an exact mass above which that object must collapse to a black hole.  Said another way, any object which collapses to the point where its radius is less than a certain limit must ultimately become a black hole.  This radius is called the Schwarzschild radius (Rs), and it is given by the following equation:

Rs = 2MG/c^2

where M is the mass of the object, G is the gravitational constant, and c is the speed of light.  If you plug in values for the constants G and c and use solar masses for M and km for Rs, this equation reduces to the following rather simple form:

Rs = 2.95*M(solar masses) km

So, for a star with the same mass as our Sun, the Schwarzschild radius is about 3 km, or about 2 miles.  In general, stars with final masses in the range 2 to 3 solar masses are believed to ultimately collapse to a black hole.

Jeff Mangum