There are so many arguments and debates related to the detection of stealth fighters are happening around. Here we are presenting a simple method to find the detection range of radars against stealth fighters.
Below you can see the radar equation, various parameters that affect the range of radar and how these variables individually affect the detection range. 

R max = 4th root of ((Pt * G2*lamda 2 * RCS) / ((4 Pie) 3 * P Min))
The variables in the above equation are constant and radar dependent except target RCS.

​The Predator UAV is a medium-altitude; long-range aircraft that operates much like any other small plane. These high-tech aircraft, controlled by a crew miles away from the dangers of combat, are capable of reconnaissance, combat and support roles in the hairiest of battles. In a worst-case scenario, if a Predator is lost in battle, military personal can simply "crack another one out of the box" and have it up in the air shortly -- and that's without the trauma of casualties or prisoners normally associated with an aircraft going down.

​The AN/APG-77 is a multifunction Low probability of intercept radar installed on the F-22 Raptor fighter aircraft. It is solid-state, active electronically scanned array (AESA) radar. The APG-77(V) radar for the F-22 is based on the successful APG-66/68/80(V) family of fire control radars. It is a multifunction solid-state, active electronically scanned array (AESA) Low probability of intercept radar installed on the F-22 Raptor. It provides 120° field of view in azimuth and elevation.  The active electronically scanned array (AESA) is a fixed, active array consisting of  1956 transmit/receive modules module low-power X-band transmit or receive modules that are electronically scanned or "steered," with no mechanical movement, each about the size of a gum stick. The separate transmitter and receiver for each radiating element results in increased agility, low radar cross-section, and wide bandwidth.
 
Its fast phase shifting and a lower level of energy is radiated by the side lobes, eliminating the spillover common to feed horn/reflector antennas. This makes the radar less detectable and reduces ground clutter. The APG-77(V) does not have a main processor of its own. Instead, two central integrated processors (CIPs), which can each process 700 million instructions per second with growth capacity up to 2,200 million, integrate the radar with other sensors and the electronic warfare systems on the F-22.

​Stealth is the corner stone of 5th gen air fighters.  Stealth tech also called Low Observable (lo) tech is a collection of techniques that makes objects less visible to radar, infrared, sonar and other detection methods. Stealth d doesn't mean it is invisible stealth is used to delay the detection as far as possible. Stealth is applicable to aircraft's  ships, submarines, missiles, satellites & even personals too. Here we only talk about stealth aircraft's.
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Before continuing we are like to give a small description about how a radar works makes further reading easier. The basic idea is the radar antenna to send out a burst of radio energy, which is then reflected back by any object it happens to encounter. The radar antenna measures the time it takes for the reflection to arrive, and with that information can tell how far away the object is.The metal body of an airplane is very good at reflecting radar signals, and this makes it easy to find and track airplanes with radar equipment.
 
One of the main focuses while developing a 5th gen fighter is reducing the Radar Cross Section (RCS) thus improving the stealth capabilities of the fighter. RCS is a measure of how detectable an object is with radar. A larger RCS indicates that an object is more easily detected