I²C Pull-up Resistor
R_max = t_rise / (0.8473 × C_bus)
Quick answer
This calculator solves R_max = t_rise / (0.8473 × C_bus) for Pull-up Resistance. With Rise Time 10 ns, Bus Capacitance 100 pF, the result is 118 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
I²C uses open-drain outputs with external pull-up resistors to drive the SDA and SCL lines high. The rise time depends on the RC time constant formed by the pull-up resistor and the total bus capacitance, which includes pin capacitance of all connected devices, trace capacitance, and any protection circuitry. The 0.8473 factor comes from the RC charging equation solved for the time to reach the 0.7×Vdd logic high threshold from 0.3×Vdd. Too large a resistor gives slow rise times that violate the I²C specification, while too small a resistor exceeds the sink current capability of the open-drain outputs.
Variables
- R — Maximum pull-up resistance (Ω)
- t_rise — Maximum allowed rise time (s)
- C_bus — Total bus capacitance (F)
Practical Notes
I²C standard mode allows 1000 ns rise time with 400 pF max bus capacitance, yielding ~2.95 kΩ max pull-up. Fast mode (400 kHz) allows 300 ns, yielding ~880Ω. A typical starting point is 4.7 kΩ for standard mode and 2.2 kΩ for fast mode. The minimum pull-up resistance is limited by the 3 mA sink current specification.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R | Pull-up Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| t_rise | Rise Time | ns | ps, ns, µs, ms, s, min, h |
| C_bus | Bus Capacitance | pF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Rise Time 10 ns, Bus Capacitance 100 pF
- 2. The relation: R_max = t_rise / (0.8473 × C_bus)
- 3. Substitute: t_rise = 10 ns, C_bus = 100 pF
- 4. Result: Pull-up Resistance = 118 Ω
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 120 Ω | 1.7% |
| E24 | 120 Ω | 1.7% |
Worked examples
Minimum range
Given: Rise Time 100 ps, Bus Capacitance 1 pF
Result: Pull-up Resistance = 118 Ω
Low range
Given: Rise Time 1 ns, Bus Capacitance 10 pF
Result: Pull-up Resistance = 118 Ω
Typical
Given: Rise Time 10 ns, Bus Capacitance 100 pF
Result: Pull-up Resistance = 118 Ω
High range
Given: Rise Time 100 ns, Bus Capacitance 1 nF
Result: Pull-up Resistance = 118 Ω
Maximum range
Given: Rise Time 1 µs, Bus Capacitance 10 nF
Result: Pull-up Resistance = 118 Ω
Solving for each variable
Solve for Pull-up Resistance
Rise Time 100 ps, Bus Capacitance 1 pF → 118 Ω
Solve for Rise Time
Pull-up Resistance 1 Ω, Bus Capacitance 1 pF → 0.8473 ps
Solve for Bus Capacitance
Pull-up Resistance 1 Ω, Rise Time 100 ps → 118 pF
How Pull-up Resistance changes with Rise Time
| Rise Time (input) | Pull-up Resistance (result) |
|---|---|
| 1 ns | 11.8 Ω |
| 2.5 ns | 29.51 Ω |
| 5 ns | 59.01 Ω |
| 7.5 ns | 88.52 Ω |
| 10 ns | 118 Ω |
| 15 ns | 0.177 kΩ |
| 20 ns | 0.236 kΩ |
| 40 ns | 0.4721 kΩ |
| 70 ns | 0.8262 kΩ |
| 100 ns | 1.18 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 118000 |
| Ω | 118 |
| kΩ | 0.118 |
| MΩ | 0.000118 |
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<p><a href="https://vbatpower.com/formulas/i2c-pullup/">I²C Pull-up Resistor</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate I²C Pull-up Resistor?
Use R_max = t_rise / (0.8473 × C_bus). With Rise Time 10 ns, Bus Capacitance 100 pF, Pull-up Resistance works out to 118 Ω.
What is the formula for I²C Pull-up Resistor?
The formula is R_max = t_rise / (0.8473 × C_bus). I²C uses open-drain outputs with external pull-up resistors to drive the SDA and SCL lines high.
How do you find Rise Time when you know the other values?
Rearrange for Rise Time: with Pull-up Resistance 1 Ω, Bus Capacitance 1 pF, Rise Time is 0.8473 ps.
How do you find Bus Capacitance when you know the other values?
Rearrange for Bus Capacitance: with Pull-up Resistance 1 Ω, Rise Time 100 ps, Bus Capacitance is 118 pF.
What units does I²C Pull-up Resistor use?
Pull-up Resistance is shown in mΩ, Ω, kΩ, MΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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