Voltage Divider Calculator

The voltage divider formula

Two resistors in series across a supply, with the output taken from the junction between them:

Vout = Vin × R2 / (R1 + R2)

R1 is the top resistor, between the input and the output node; R2 is the bottom one, between the output node and ground. The output is the input scaled by R2’s share of the total resistance, which is all thevoltage divider rule says: in a series chain, the voltage across any part is the whole voltage times that part’s share of the resistance. British textbooks call the circuit apotential divider; it is the same two resistors.

The three rearrangements are the ones you actually reach for, and the tool solves all of them:

• R1 = R2 × (Vin − Vout) / Vout — the top resistor for a wanted output
• R2 = R1 × Vout / (Vin − Vout) — the bottom one
• Vin = Vout × (R1 + R2) / R2 — what the input must have been

A number to anchor it: 10 k on top, 10 k on the bottom, 5 V in. R2’s share is 10/20, so Vout is 2.5 V. Make the bottom one 20 k and its share is 20/30, so Vout is 3.33 V. Notice that only the ratioappears — 10 k and 20 k give the same output as 100 k and 200 k, or 1 k and 2 k. Everything that makes one of those three the right choice and the other two wrong is current, loading and noise, which is the rest of this page.

The ratio is not the answer

The divider equation takes one line: Vout = Vin × R2 / (R1 + R2). Any calculator can solve it for a ratio. The work starts after that, because a ratio is not a part number. Wanting 3.3 V from 5 V with a 10k bottom resistor calls for R1 = 5151.5 Ω, and that resistor does not exist. You will fit 5.1k or 5.6k, and the question that matters is what the output becomes when you do.

This tool searches the standard values a series actually offers, pairs each R2 with the nearest real R1, and ranks the pairs by how close the nominal output lands. The answer is two resistors you can order and the voltage you will actually get.

Why 4.7k exists and 4.5k does not

Resistors are made in preferred values defined by IEC 60063, spaced roughly evenly on a logarithmic scale so that each value's tolerance band just about meets its neighbour's. E24 puts 24 values in each decade and is sold at ±5%; E96 puts 96 in a decade at ±1%. That is why the familiar numbers are 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7 and so on, and why a 4.5k resistor is not something you will find in a drawer.

One detail worth knowing: the coarse series were rounded by hand long before the geometric formula was standardised, so E24 has 2.7 and 4.7 where the formula would give 2.6 and 4.6. A calculator that generates E24 from the formula produces values nobody sells. The tables here are the published ones.

Tolerance is the number that bites

The nominal error — the difference between the target and what the marked values produce — is often a fraction of a percent and easy to feel good about. The tolerance band is a different matter. Two ±5% parts can each be anywhere within their band, and when R2 is high and R1 is low the output climbs; the opposite corner drops it. For 5.1k over 10k from 5 V the nominal output is 3.311 V, but the worst-case range is 3.198 V to 3.421 V — a spread of more than 6%.

If the output sets a reference, a threshold, or a supply rail for something that cares, that band is the specification, not the nominal. Switching to ±1% parts narrows it to about 1.3%. The tool shows both so the choice is made with the numbers in front of you rather than discovered on the bench.

A divider is not a source

Everything you connect to the output sits in parallel with R2. A 10k load across a 10k R2 halves the bottom leg and the output drops well below what was calculated. The figure to check is the output impedance, which is R1 in parallel with R2; the load should be at least ten times larger for the calculated voltage to survive within a few percent.

The same rule catches an ADC. A microcontroller's sample-and-hold input has to charge its internal capacitor through whatever impedance feeds it, and many parts specify a maximum source impedance of a few kilohms for full accuracy at full speed. A divider built from 100k parts to save current will read low unless a buffer or a capacitor at the input, or a slower sampling rate, gives it time.

Current and power are the other constraint

Pushing the resistances down fixes the loading problem and creates a different one. The divider draws Vin / (R1 + R2) all the time, whether or not anything reads the output. On a battery-powered board a 1k divider across 3.7 V is 1.2 mA continuously, which can be more than the microcontroller sleeping. On a 24 V industrial input a 100 Ω pair dissipates over 5 W and needs a resistor rated for it.

That is why the tool asks for the R2 range instead of guessing. 1k to 100k covers nearly everything; below it you are paying in current and heat, above it in accuracy at the load.

Scaling an ADC reading in firmware

When the divider feeds an ADC, the code that converts counts back to volts should use the resistors that were fitted, not the ratio that was wanted. With 5.1k and 10k the scale factor is (5.1 + 10) / 10 = 1.51, not 1.515; using the ideal ratio bakes the nominal error into every reading. Better still is to calibrate once against a known voltage and store the measured factor, which absorbs the tolerance of the actual parts on the actual board.

For the arithmetic on the microcontroller side, the Q format converter shows what a scale factor becomes once it is stored as a fixed-point constant, and the IEEE 754 converter shows the exact value a float holds.