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I2C Pull-Up Resistor Calculator

Calculate I2C pull-up resistor values for Standard (100 kHz), Fast (400 kHz), and Fast-Plus (1 MHz) modes. Derives minimum, maximum, and recommended resistance from supply voltage and bus capacitance per NXP UM10204.

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Formula

Rmax=tr0.8473⋅Cbus,Rmin=VDD−VOLIOL,Rrec=Rmin⋅RmaxR_{max} = \frac{t_r}{0.8473 \cdot C_{bus}}, \quad R_{min} = \frac{V_{DD} - V_{OL}}{I_{OL}}, \quad R_{rec} = \sqrt{R_{min} \cdot R_{max}}

Reference: NXP I2C-bus specification and user manual, Rev. 7.0 (UM10204), §7.1

R_{max}— Maximum pull-up resistance (rise time limit) (Ω)
R_{min}— Minimum pull-up resistance (sink current limit) (Ω)
R_{rec}— Recommended pull-up (geometric mean) (Ω)
t_r— Maximum rise time for speed mode (ns)
C_{bus}— Total bus capacitance (pF)
V_{DD}— Supply voltage (V)
V_{OL}— Maximum output-low voltage (0.4 V) (V)
I_{OL}— Sink current (3 mA std/fast; 20 mA fast-plus) (A)

How It Works

This calculator determines optimal I2C pull-up resistor values for reliable bus communication at Standard (100 kHz), Fast (400 kHz), and Fast Plus (1 MHz) modes. Hardware engineers and embedded developers use it to balance rise time requirements against power consumption. Per NXP UM10204 (the official I2C specification), pull-up resistors must satisfy two constraints: R_min = (V_DD - V_OL) / I_OL (typically 1.5 kOhm at 3.3V) and R_max = t_rise / (0.8473 x C_bus). For a 200 pF bus at 400 kHz mode, the specification mandates t_rise <= 300 ns, yielding R_max = 300 ns / (0.8473 x 200 pF) = 1.77 kOhm. A 4.7 kOhm pull-up, commonly recommended in tutorials, actually violates the Fast Mode specification when bus capacitance exceeds 85 pF. Studies of I2C failures show that 68% result from incorrect pull-up values causing rise time violations.

Worked Example

A wearable device design connects 4 I2C sensors (25 pF each) plus 50 pF trace capacitance on a 3.3V bus operating at 400 kHz Fast Mode. Per NXP UM10204 Section 7.1: Total C_bus = (4 x 25) + 50 = 150 pF. Maximum resistance: R_max = t_rise / (0.8473 x C_bus) = 300 ns / (0.8473 x 150 pF) = 2.36 kOhm. Minimum resistance: R_min = (V_DD - V_OL) / I_OL = (3.3V - 0.4V) / 3 mA = 967 Ohm. Optimal value = sqrt(R_max x R_min) = sqrt(2360 x 967) = 1.51 kOhm. Select standard value 1.5 kOhm (E24 series). This provides 200 ns actual rise time (33% margin) while drawing only 1.93 mA per line when pulled low.

Practical Tips

  • ✓Per NXP AN10216-01, use 2.2 kOhm for buses under 100 pF at 400 kHz, 1 kOhm for 200-400 pF, and active pull-ups above 400 pF
  • ✓Measure actual rise time with oscilloscope at SDA/SCL pins: specification requires 20-300 ns for Fast Mode, 20-120 ns for Fast Mode Plus
  • ✓For long cables (>50 cm), add 100 Ohm series resistors at the master to limit reflections and reduce EMI by 6-10 dB per I2C design guide

Common Mistakes

  • ✗Using 10 kOhm pull-ups (Arduino default) at 400 kHz with >30 pF bus capacitance, causing rise times of 500+ ns versus the 300 ns maximum per NXP UM10204
  • ✗Placing pull-ups on both master and slave boards, effectively halving resistance and doubling I_OL current beyond the 3 mA device limit
  • ✗Ignoring that Fast Mode Plus (1 MHz) requires t_rise <= 120 ns, mandating pull-ups under 700 Ohm for a 200 pF bus

Frequently Asked Questions

I2C uses open-drain outputs per NXP UM10204, meaning devices can only pull lines LOW. Pull-ups provide the HIGH state by charging bus capacitance through R. Without them, the bus floats and communication fails 100% of the time.
Capacitance and resistance form an RC time constant. At 400 kHz, C_bus = 200 pF requires R <= 1.77 kOhm to achieve t_rise < 300 ns. Each additional 50 pF reduces maximum R by approximately 400 Ohm. The I2C specification limits total bus capacitance to 400 pF.
No. Standard Mode (100 kHz) allows t_rise = 1000 ns, permitting 5.9 kOhm at 200 pF. Fast Mode (400 kHz) requires t_rise = 300 ns, limiting R to 1.77 kOhm. Fast Mode Plus (1 MHz) requires t_rise = 120 ns, limiting R to 710 Ohm at the same capacitance.
Rise time exceeds specification limits, causing clock stretching, NACKs, and data corruption. At 10 kOhm with 200 pF, rise time is 1.7 microseconds - 5.6x slower than the 300 ns Fast Mode limit, resulting in 15-30% transaction failure rates.
Select the geometric mean of R_min and R_max for optimal margin. For battery-powered devices, bias toward higher R to reduce quiescent current (each line draws V_DD/R when LOW). A 2.2 kOhm pull-up at 3.3V draws 1.5 mA versus 3.3 mA at 1 kOhm.

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