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Electrical calculator

Voltage Divider Calculator

Solve a two-resistor voltage divider: enter exactly three of Vin, R1, R2, and Vout to find the fourth. Also reports current, power, ratio, and Rth. Try it free.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (solve-vout, solve-r, invalid-domain) · Matrix
Known limitations
  • No load current on tap; R1+R2>0 when solving Vout
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Unloaded two-resistor divider: solve exactly one of Vin, R1, R2, Vout from the other three; also I, power, divider ratio, and Rth.
Scope
No load on Vout
Verification
Engine tested · Source checked · v1.5.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.5.1 · CVP protocol 1.0.0-proposed
CVP identity
11/11 property · digest 634843a750b6
Legacy regression
28/28 tests · Production surface contract 4/4
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
3/3 golden · 8/8 CVP boundary · 8/8 invalid · 11/11 property · 1/1 cross-interface · 4/4 CVP contract · Manifest
Sources
Sources
Evidence
9 legacy golden · 8 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 8/8 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.5.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Output voltageVout = Vin × R2 / (R1 + R2)
Solve R2R2 = R1 × Vout / (Vin − Vout)
Solve R1R1 = R2 × (Vin − Vout) / Vout
Solve VinVin = Vout × (R1 + R2) / R2
CurrentI = Vin / (R1 + R2)
Divider ratiok = R2 / (R1 + R2)
Output resistanceRth = R1 ∥ R2 = R1 R2 / (R1 + R2)
iUnloaded divider only. A load RL on Vout forms a voltage divider with Rth = R1∥R2; relative droop is Rth/(Rth+RL). Enter R1/R2 in Ω, kΩ, or MΩ (API/share URLs stay in ohms). For AC with capacitors, use impedances — this tool is resistive DC. Invalid Vin/Vout combinations, zero resistance sums, and four-value payloads are rejected with stable API error codes (not fake R=0).

How to use

1

Enter exactly three values

Fill Vin, R1, R2, and/or Vout — leave exactly one blank to solve for it.

2

Use engineering units

R1 and R2 accept Ω, kΩ, or MΩ. Share URLs and the API use ohms.

3

Read Vout, current, Rth, and power

Result shows the solved quantity plus divider ratio, series current, Thevenin output resistance, and dissipation.

Example calculations

Common configurations with formula and result.

ϟ

5 V → 3.3 V logic

Vin = 5 V · R1 = 1 kΩ · R2 = 2 kΩ

Vout = 5×2000/(1000+2000)
3.333 V
ϟ

Half voltage

9 V · R1 = R2 = 10 kΩ

Vout = 9×0.5
4.5 V
ϟ

Solve R2 for 3.3 V

Vin = 5 V · R1 = 1 kΩ · Vout = 3.3 V

R2 = 1000×3.3/(5−3.3)
≈ 1.94 kΩ (use 2 kΩ)
ϟ

Battery sense tap

Vin = 12 V · R1 = 10 kΩ · R2 = 10 kΩ

Vout = 6 V
6 V · I = 0.6 mA

Common divider examples (unloaded)

Common values at a glance.

VinR1R2Vout
5 V1 kΩ2 kΩ3.33 V
5 V1 kΩ1.94 kΩ3.30 V
9 V10 kΩ10 kΩ4.5 V
12 V10 kΩ10 kΩ6 V
3.3 V10 kΩ20 kΩ2.2 V
i Pick nearest E24/E96 resistor to the calculated value. Prefer higher kΩ for lower idle current when the ADC/load allows.

Voltage Divider calculator specification

Version 1.5.1 · Engine tested

Calculation status

Review policy · Evidence

Definition
A resistive voltage divider uses two series resistors to produce a lower DC voltage from a higher source. With R1 from Vin to the tap and R2 from the tap to ground, Vout across R2 is Vin × R2 / (R1 + R2). Enter exactly three of Vin, R1, R2, and Vout to solve the fourth. The tool also reports series current, resistor power, divider ratio, and Thevenin output resistance Rth = R1∥R2 (unloaded).
What it calculates
Unloaded two-resistor divider: solve exactly one of Vin, R1, R2, Vout from the other three; also I, power, divider ratio, and Rth.
Inputs
  • Exactly three of: Vin (V), R1 (Ω), R2 (Ω), Vout (V) — all ≥ 0
Outputs
  • Vin, R1, R2, Vout (solved set)
  • Series current I (A)
  • Power in R1, R2, and total (W)
  • Divider ratio k = R2/(R1+R2)
  • Thevenin output resistance Rth = R1∥R2 (Ω)
Formula
Vout=Vin·R2/(R1+R2); I=Vin/(R1+R2); Rth=R1∥R2; P=I²R
Assumptions
  • No load on Vout
  • DC / resistive
  • R1 from Vin to tap; R2 from tap to ground
Units
  • V, Ω → V, A, W, and Rth in Ω; ratio is dimensionless
Boundary conditions
  • Fewer than three of Vin,R1,R2,Vout → NEEDS_THREE_INPUTS
  • All four of Vin,R1,R2,Vout → TOO_MANY_INPUTS
  • Negative inputs → VALUE_MUST_BE_NON_NEGATIVE
  • Non-finite inputs → INVALID_NUMBER
  • Solving R1/R2 when not (Vin > Vout > 0) → INVALID_DIVIDER_VOLTAGES
  • R1+R2=0 when solving Vout, or R2=0 when solving Vin → RESISTANCE_MUST_BE_POSITIVE
  • Vin=0 with R1,R2>0 → Vout=0, I=0 (valid)
Example
5 V, 1 kΩ, 2 kΩ → Vout = 3.333 V · I ≈ 1.667 mA · Rth ≈ 667 Ω
Validation cases

14 published on this page · 28/28 tests · Production surface contract 4/4 · View evidence

  • 5 V, 1000 Ω, 2000 Ω → Vout = 3.333 V · I ≈ 1.667 mA · Rth ≈ 667 Ω
  • 9 V, 10 kΩ, 10 kΩ → Vout = 4.5 V
  • 5 V, 1 kΩ, Vout 3.3 V → R2 → ≈ 1941 Ω
  • 12 V, 4 kΩ, 4 kΩ → Vout = 6 V (equal divider)
  • 10 V, 1000 Ω, 2000 Ω (2× Vin of 5 V) → Vout = 6.667 V (linear in Vin)
  • 5 V, 1 kΩ, Vout 3.333 V → R2 → ≈ 2000 Ω (round-trip)
  • 0 V Vin, 1 kΩ, 2 kΩ → Vout = 0 V · I = 0
  • 5 V, R1=0, R2=0 → error RESISTANCE_MUST_BE_POSITIVE
  • 5 V, 1 kΩ, Vout 6 V → R2 → error INVALID_DIVIDER_VOLTAGES
  • 5 V, R1=-1000, R2=2000 → error VALUE_MUST_BE_NON_NEGATIVE
  • 5 V, 1 kΩ only (two inputs) → error NEEDS_THREE_INPUTS
  • Empty inputs → error NEEDS_THREE_INPUTS
  • 5 V, 1 kΩ, 2 kΩ, and Vout 3.3 V (four inputs) → error TOO_MANY_INPUTS
  • Vout 3.333 V, R1 1 kΩ, R2 2 kΩ → Vin → Vin = 5 V
Sources
Calculation version
1.5.1

Background

Interpretation and common distinctions.

A voltage divider (potential divider) turns a higher source voltage Vin into a lower output Vout using two series resistors.

Vₒᵤₜ = Vᵢₙ × (R₂)/(R₁ + R₂)

Default example: 5 V · R1 = 1 kΩ · R2 = 2 kΩ → Vout ≈ 3.333 V, Rth ≈ 667 Ω (common 5 V → ~3.3 V logic level).

The unloaded output resistance is the parallel pair:

Rₜₕ = R₁ parallel R₂ = (R₁ R₂)/(R₁+R₂)

A load R_L on Vout drops the tap by Rₜₕ/(Rₜₕ+R_L). For about 1% droop, R_L gtrsim 99 Rₜₕ.

Circuit

5 V
 │
1 kΩ
 │──── 3.333 V
2 kΩ
 │
GND
  • R1 — upper resistor (from Vin to the tap)
  • R2 — lower resistor (tap to ground); Vout is across R2
  • Rth — Thevenin resistance seen looking into the tap, R₁parallel R₂

Supported and not supported

Supported

  • Unloaded two-resistor DC / resistive dividers
  • Solve exactly one of Vin, R1, R2, Vout from the other three
  • Series current, resistor power, divider ratio, and output resistance Rth
  • Shareable query URLs (Vin, R1, R2, Vout) and REST/OpenAPI/MCP via electrical.voltage_divider

Not supported

  • Loaded dividers (ADC/GPIO/meter loading R2) — Rth is reported so you can estimate droop, but V(loaded) is not computed
  • Four-value consistency check (all four of Vin, R1, R2, Vout → TOO_MANY_INPUTS)
  • Capacitive, inductive, or RF impedance dividers
  • Multi-tap / more than two resistors
  • Tolerance stack-up, noise, or Vin source-resistance models
  • Safety / compliance cable or protection design

Design tips

  • Loading: Compare R_L to Rth, not to R2. Relative droop is Rₜₕ/(Rₜₕ+R_L). Buffer the tap when the load is not ≫ Rth.
  • Idle current: Larger R1+R2 wastes less power but increases Rth, noise, and error from leakage.
  • Tolerance: 1% resistors stay closer to the calculated Vout than 5%.
  • Power: Check P1 and P2 against the resistor wattage rating.

Agent / API notes

Capability id: electrical.voltage_divider · tool id: voltage-divider · pin calculation_version: 1.5.1.

Canonical Agent input is exactly three of Vin, R1, R2, Vout (JSON Schema oneOf the four solve modes). Stable error codes include NEEDS_THREE_INPUTS, TOO_MANY_INPUTS, INVALID_DIVIDER_VOLTAGES, RESISTANCE_MUST_BE_POSITIVE, VALUE_MUST_BE_NON_NEGATIVE, and INVALID_NUMBER.

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Frequently asked questions

Key distinctions behind the calculation.

What is a voltage divider?

Two (or more) resistors in series that split a source voltage into a smaller tap voltage. The classic formula is Vout = Vin × R2 / (R1 + R2), with Vout taken across R2 to ground.

How do I use this calculator?

Enter exactly three of Vin, R1, R2, and Vout. The fourth is calculated. With Vin, R1, and R2 filled, you get Vout plus series current, divider ratio, Rth, and resistor power. All four fields at once are rejected (TOO_MANY_INPUTS).

Which resistor is R1 and which is R2?

R1 is the upper resistor (from Vin to the output node). R2 is the lower resistor (from the output node to ground). Vout is across R2.

Why is my measured Vout lower than calculated?

Usually loading: anything on Vout (ADC, GPIO, meter) parallels R2 and lowers the tap. The relevant impedance is the divider Thevenin resistance Rth = R1∥R2, not R2 alone. Relative droop is Rth/(Rth+RL). For about 1% droop, RL ≳ 99×Rth. A “10× R2” rule is not a universal margin — e.g. 1 kΩ / 2 kΩ with RL = 20 kΩ (10×R2) still drops Vout by about 3.2%.

How do I choose resistor values?

Fix a convenient R1 (e.g. 1 kΩ or 10 kΩ), solve for R2, then pick the nearest standard value. Higher resistances draw less current but are noisier and more sensitive to leakage; check resistor power rating.

Can I use this for AC?

For purely resistive AC at low frequency, the same ratio applies to RMS voltages. Capacitive dividers and RF need impedance-based design — not covered here.

What about power rating?

P = I²R for each resistor (shown in the result). Choose a resistor wattage with margin above the calculated dissipation.

What if Vout ≥ Vin when solving for a resistor?

The calculator and API reject the request with INVALID_DIVIDER_VOLTAGES. They do not return a fake R = 0.

What if I enter fewer than three values?

UI and API require exactly three of Vin, R1, R2, Vout. Fewer inputs return NEEDS_THREE_INPUTS. All four return TOO_MANY_INPUTS — this version does not treat four values as a consistency check.