LED spec in lm and mcd

[Wilson__]

Why differnt LED brightness specification are in

(a) Luminous Flux (lm) (b) Luminous Intensity (mcd)?   

How to compare and choose the brigher LED for same current consumption?

Many thanks

[Nominal Animal]

Given luminous intensity \$I_v\$ in candelas (1 cd = 1000 mcd) and solid angle in steradians (full sphere being \$4 \pi\$, half-sphere \$2 \pi\$ steradians), luminous flux \$\Phi_v\$ is \$\Phi_v = I_v \Omega\$.

For an omnidirectional (spherical) uniform bulb, luminous flux is about 0.012566 lm/mcd.
For a bulb emitting light at uniform intensity to half-space, luminous flux is about 0.0062832 lm/mcd.

For LEDs, luminous intensity varies depending on the direction, and luminous flux is actually an integral of the direction-dependent luminous intensity over all solid angles (all possible directions).

Technically, candelas describe the (wavelength-weighted) power emitted by the light source in a particular direction.  Solid angle describes how much of all possible directions the light source covers (the surface area of an unit-radius sphere), and luminous flux is the total amount of (wavelength-weighted) power emitted by the light source.

Thus, when listed for a LED, the figure in candelas is either a peak or average intensity, and varies depending on direction; and the flux in lumen is the overall amount of light it emits considering all directions.  The ratio of the flux to intensity, \$\Omega = \Phi_v / I_v\$, is a rough single-number description of the solid angle it emits light to, or "spread", if you will.

[Psi]

Put simply..

Lumens (lm) is the amount of total light emitted in all directions all added together.
The LED Angle does not come into it.  You can compare one leds lumens to another's lumens to determine which one is more efficient (more light for same power in)

cd/mcd is the amount of light that hits a fixed point directly in front of the LED.  So a narrow angle LED (led with lens) focuses and concentrates its emitted light into a beam. eg The same LED die with a 20deg lens will have a much higher mcd than that led with a 100deg lens even when they are both the same lumens.
You can only compare a mcd values between LEDs with the same angle.

You can use these online calculators to convert mcd + angle into lumens and back
but be aware the conversion is not perfect, there is some error.

https://www.rapidtables.com/calc/light/mcd-to-lumen-calculator.html
https://www.rapidtables.com/calc/light/lumen-to-mcd-calculator.html