Voltage Divider Calculator (E12, E24, E96)

Formulas

• Vout = Vin × R2 ÷ (R1 + R2)
• R2 = R1 × Vout ÷ (Vin − Vout), R1 = R2 × (Vin − Vout) ÷ Vout
• With a load, replace R2 by R2 ∥ RL = R2 × RL ÷ (R2 + RL)
• Current I = Vin ÷ (R1 + R2), power P = I² × R
• Output (Thévenin) impedance = R1 ∥ R2

E12, E24 and E96 standard resistor values

• Resistors come in standard values that split each decade geometrically. The series are defined in IEC 60063: E12 has 12 values, E24 has 24, E96 has 96. The denser the series, the closer neighbours are, so you can get nearer the value you want. Which series a maker sells in which tolerance is in the resistor datasheet.
• Every E96 value equals 10^(i/96) rounded to three digits, but in E24 the values 27, 30, 33, 36, 39, 43, 47 and 82 differ from the computed ones (26, 29, 32, 35, 38, 42, 46, 83). So use the table, not a formula — this calculator uses the values from Vishay's IEC 60063 table.
• Two standard values rarely give the exact ratio. «Standard-value pairs» above sweeps R2 through the series, tries the standard values just below and above the R1 it needs, and lists the pairs by error.

E24 values (E12 in bold)

1.0 · 1.1 · 1.2 · 1.3 · 1.5 · 1.6 · 1.8 · 2.0 · 2.2 · 2.4 · 2.7 · 3.0 · 3.3 · 3.6 · 3.9 · 4.3 · 4.7 · 5.1 · 5.6 · 6.2 · 6.8 · 7.5 · 8.2 · 9.1

E96 values

Loading and ADC inputs

• Whatever you connect to the output appears in parallel with R2 and pulls the output down. If the load is not much larger than R2, enter it under «Load resistance RL».
• An MCU ADC must charge an internal capacitor at each sample. The ATmega328P datasheet (§23.6.1) says its ADC «is optimized for analog signals with an output impedance of approximately 10 kΩ or less»; above that, the sampling time depends on how long the source takes to charge the 14 pF S/H capacitor. Keep the divider's output impedance (R1 ∥ R2) in that range, or add a capacitor or buffer at the output.
• A lower total resistance lowers the output impedance but raises current and heat: 24 V across 1 kΩ + 1 kΩ is 12 mA and 144 mW per resistor — check the power rating too.

Tolerance

The output moves most when the two resistors sit at opposite ends of their tolerance. Two equal ±1 % resistors (a 1/2 divider) give about ±1 % on the output. For better accuracy use tighter parts or calibrate in software with measured values.

FAQ

Which resistors turn 10 V into 3.3 V?

In E12, R1 6.8 kΩ and R2 3.3 kΩ give about 3.267 V (−1.0 %), the closest pair. In E96 several pairs land within 0.5 %, for example R1 10.2 kΩ and R2 4.99 kΩ.

Can I use a divider for 5 V to 3.3 V?

For slowly changing analog voltages, yes. Fast or bidirectional digital signals suffer from the divider's output impedance and the input capacitance, so a level shifter is common there.

Why do E-series values go 1, 1.2, 1.5, 1.8…?

They are a geometric sequence across a decade, so neighbours are always a similar percentage apart: about 21 % in E12 and about 2.4 % in E96.

Can one resistor turn a current signal into a voltage?

A 4–20 mA signal uses a single shunt resistor (250 Ω → 1–5 V). For the ADC side of that, use the ADC resolution calculator.

For ADC counts and engineering units, use the ADC Resolution & Scaling Calculator. For NTC thermistor dividers, use the NTC Thermistor Calculator. To make one resistance value from two resistors (rather than a ratio), use the Parallel & Series Resistor Calculator.

Sources

• Vishay, Standard Series Values in a Decade for Resistances and Capacitances, E3 to E192, according to IEC 60063 (Document 28372, Rev. 22-Aug-12)
• Microchip, ATmega328P datasheet (7810D, 01/2015): §23.6.1 Analog Input Circuitry