Those tiny OLED displays are everywhere, and for good reason. They're inexpensive, simple to program, and they look good. I was interested in learning how much current they consumed so that I could better plan for battery-powered projects.

Materials Techniques :

A low-cost multimeter (with a manual scale and an assumed accuracy of +/-10% at worst).
Various OLED displays (72x40, 96x16, 128x32, 64x32, 128x64-0.96, 128x64-1.3)
Microcontroller compatible with Arduino (Adafruit nRF52840 Feather Express) and software (my ss_oled library)

What about OLED displays in both color and grayscale?

I was asked on Twitter to include a quick test of these round lcd display, so I obliged. I could tell that the power consumption was high because the controller chip gets hot to the touch even when there isn't much information displayed. I no longer have access to my SSD1351 color OLED display, but I do have an SSD1327 128x128 4-bit grayscale display to test. With the display turned off, I measured 600uA. Here are some of the values I obtained when the contrast (brightness) was set to its maximum setting:

Display filled with color at a current of 0 - 2.5mA (every pixel is off/black).
Display filled with color 1 - 85mA
Display filled with color 2 - 111mA
Display filled with color 3 - 147mA
The color 15 has been displayed on the screen (the display was reset due to my 3.3v power supply sagging).

In general, the display consumes significantly more current to achieve the same pixel brightness when compared to the monochrome SSD1306 displays.

What about real-time data writing?

In addition to the increased activity on the display controller, there will be current leaking through the pullup resistors when the SCL or SDA lines are brought low. Pullup resistors for these displays are typically 4.7KOhm, which means that while the data and clock lines are active, approximately 700uA (3.3V / 4700 ohms) will leak through them. I attempted a test in which I continuously wrote the same data to the display (using the same display and text as above). The results were a reading of 1.47mA. Different pullup resistors and different data being written will produce different results.