During the measurement of the intensity of light emitted from an LED, we have to consider the solid angle (in steradian). If we are not using an integrating sphere, then how to calculate solid angle?
Have a look at the technical guide published by Labsphere "The Radiometry of Light Emitting Diodes". It can be found at this link: http://www.labsphere.com/uploads/technical-guides/The%20Radiometry%20of%20Light%20Emitting%20Diodes%20-%20LEDs.pdf
Section 5.1 gives the formula for solid angle and Fig 4.1 shows the CIE standard setup for measuring LED intensity using a photodiode.