I2C Pull-Up Resistor Calculator Formula

Understand the math behind the i2c pull-up resistor calculator. Each variable explained with a worked example.

Use the I2C Pull-Up Resistor Calculator

Formulas Used

Minimum Resistance

r_min = (vcc - vol_max) / (iol_ma / 1000)

Maximum Resistance

r_max = rise_time_ns * 1e-9 / (0.8473 * bus_cap_pf * 1e-12)

Recommended Value

r_recommended = ((vcc - vol_max) / (iol_ma / 1000) + rise_time_ns * 1e-9 / (0.8473 * bus_cap_pf * 1e-12)) / 2

Variables

VariableDescriptionDefault
vccSupply Voltage(V)3.3
vol_maxMax Low-Level Voltage(V)0.4
iol_maSink Current Capability(mA)3
bus_cap_pfTotal Bus Capacitance(pF)200
rise_time_nsRequired Rise Time(ns)300

How It Works

I2C Pull-Up Resistor Sizing

I2C uses open-drain outputs with pull-up resistors. Too small a resistor exceeds sink current; too large slows the rise time.

Formulas

R_min = (VCC - V_OL) / I_OL (current limit)

R_max = t_rise / (0.8473 x C_bus) (rise time limit)

The 0.8473 factor comes from the RC time constant to reach 0.7 x VCC.

Choose a standard value between R_min and R_max. Closer to R_min for faster speeds, closer to R_max for lower power.

Worked Example

3.3 V supply, standard I2C (3 mA sink, 300 ns rise time), 200 pF bus.

vcc = 3.3vol_max = 0.4iol_ma = 3bus_cap_pf = 200rise_time_ns = 300
  1. 01R_min: (3.3 - 0.4) / 0.003 = 967 ohms
  2. 02R_max: 300e-9 / (0.8473 x 200e-12) = 1770 ohms
  3. 03Recommended: (967 + 1770) / 2 = 1369 ohms
  4. 04Use nearest standard value: 1.2k or 1.5k ohms

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