Starting with a box of cheap LEDs from halfway around the planet:
Measuring the forward voltages didn’t take much effort:
The top array fed the LEDs from a bench power supply through a 470 Ω resistor, with the voltage adjusted to make the current come out right. The bottom array came from the Siglent SDM3045 multimeter’s diode test function, which goes up to 4 V while applying about 400 µA to the diode (the 20 µA header is wrong).
These numbers come into play when blinking an LED from a battery, because a battery voltage much below the Vf value won’t produce much light. It’s a happy coincidence that a single lithium cell can light a white or blue LED …
For comparison, the forward voltages from another batch of LEDs:
Those all look a bit higher at 20 mA, but everything about the measurements is different, so who knows?