The Schwarzschild Radius calculator computes the Schwarzschild Radius based on the mass (M) of the object (e.g. black hole), the speed of light and the universal gravity constant.
INSTRUCTIONS: Choose units and enter the following:
Schwarzchild Radius (R_{s}): The calculator returns the radius in meters. However, this can be automatically converted to compatible units via the pulldown menu.
The formula for the Schwarzschild Radius is:
where:
The Schwarzchild Radius, R_{S}, is the radius defining the maximum size of a star necessary to create a black hole. In other words, a mass must collapse to a size having a radius smaller than this radius to become a black hole.
Any mass with a radius less than the Schwarzchild Radius will have an escape velocity greater than the speed of light, so even light cannot escape it's gravitational grasp. The Schwarzchild Radius also defines the sphere sometimes referred to as the Event Horizon. Since light cannot escape from a black hole, a Star of this dimension has a spherical surface inside of which we cannot see events occurring.
Input to this equation is M, the mass of the star.
Current theory suggests that a burnedout star of approximately three times the Sun's mass will collapse under its own gravity and form a black hole. This equation then suggests that such a star, once collapsed, would have an event horizon of less than 6 miles (less than 9 kilometers).
So, what then would be the approximate density of such a threesolar mass black hole? Greater than `2E^18 "kg"/m^3`. That's more than 100,000,000,000,000 times denser than gold.
Because of the enormity of space and the size of the objects studied, the field of astronomy employs units not commonly used in everyday life. Nonetheless, these units do translate into common units at a grand scale, and vCalc provides automatic conversions between units for calculator inputs and answers via the pulldown menus. The following is a brief description on the distance, mass and time units employed in the field of astronomy
Astronomical Unit (au): Within our solar system, a common measure of distance is au, which stands for astronomical units. A single astronomical unit is the mean distance from the Sun's center to the center of the Earth.
Astronomical Unit (au)  Distance from Sun (au) 



Light Travel in Time: Light is a primary observable when studying celestial bodies. For this reason, the distance to these objects are measured in the amount of time it would take light to travel from there to the Earth. We can say that an object is one lightyear away, and that means that the object is at a distance where it took an entire year for light from the object to travel to Earth. Since the speed of light is 299,792,458.0 meters per second, one can compute the distance equal to a light year as follows:
1 light year = 299,792,458.0 (meters / second) x 31,536,000 (seconds / year) = 9,460,528,405,000,000 meters
The same exercise can be used for light traveling shorter periods of times, light seconds, light minutes, light hours and light days. Since even these units are not enough when computing distances across the universe, there is also a light relative distance of kilolight years (1000 light years), or the distance light travels in a thousand years!
Light Second  Light Minute  Light Hour  Light Day  Light Year  KiloLight Year 

299,786 km 186,278 miles 0.002 au 
17,987,163 km 11,176,705 miles 0.12023 au 
1,079,229,797 km 670,602,305 miles 7.214 au 
25,901,515,140 km 16,094,455,343 miles 173.14 au 
9,460,528,405,000 km 5,878,499,814,210 miles 63,240 au 0.306 parsecs 
9,460,528,405,000,000 km 5,878,499,814,210,000 miles 63,240,000 au 306 parsecs 
Angle Shift Seen from Earth: Because the Earth goes around the Sun, our observation of distant objects such as stars results in an angular shift when observed at opposite sides of the elliptical orbit. This shift is used as the basis of a unit knows as a parsec. A parsec was traditionally defined as the distance where one astronomical unit subtends an angle of one arcsecond. A parsec was redefined in 2015 to 648000/π astronomical units. Proxima Centauri, is the nearest star to the Sun and is approximately 1.3 parsecs (4.2 lightyears) from the Sun. A megaparsec is a million parsecs.
Parsec  Megaparsec 



Astronomical units also apply to the mass of enormous objects such as moons, planets and stars. For this reason, astronomy also employs mass units that compare other objects to ones familiar to us. For example, stars are often measured in mass units of solar masses. This is a comparison of their mass to the mass of our sun (one solar_mass). For planets, astronomers use Earth masses and Jupiter masses for understanding the relative size of rocky planets and gas giants.
Earth Masses  Jupiter Masses  Solar Masses 




Astronomers use the same time units as everyone else, from the very small nanoseconds, to seconds, minutes, hours, days and years. This is true with two exceptions known as sidereal days and sidereal years. These refer to time relative to the celestial objects (the fixed stars). The Earth rotates every 24 hours relative to the Sun. But we are moving in a circle around the Sun. In comparison, the Earth rotates every 23 hours, 56 minutes and 4.0905 seconds (23.9344696 hours) compared to the stars in the celestial sphere. This is known as a sidereal day.
In the same vein, a sidereal year is the time it takes the Earth to complete one orbit around the Sun relative to the celestial sphere. Where a year is 365 days, a sidereal year is 365.256363004 days, or 1,224.5 seconds more than a calendar year.
Sidereal Day  Sidereal Year 


