Calculate resistor voltage divider outputs, find R1 or R2 for a target voltage, solve loaded dividers with Thevenin equivalents, balance Wheatstone bridges, and design Zener regulators — 5 modes, Ohm’s Law verified.
Vout = Vin × R2 / (R1 + R2) — R1 is top (Vin to Vout), R2 is bottom (Vout to GND):
Supply or source voltageEnter valid Vin.
Resistor between Vin and VoutEnter valid R1.
Resistor between Vout and GNDEnter valid R2.
Design a divider for a specific output voltage — enter Vin, Vout, and one resistor value:
Supply voltageEnter valid Vin.
Must be less than VinVout must be > 0 and < Vin.
Which resistor to calculateSelect option.
Enter the known resistor valueEnter valid resistor value.
Loaded divider: R2 and RL are in parallel. Thevenin equivalent calculated automatically:
Input voltageEnter valid Vin.
Top resistorEnter valid R1.
Bottom resistorEnter valid R2.
Load resistance at VoutEnter valid RL.
Wheatstone bridge: R1–R2 form one divider, R3–R4 the other. Bridge balances when R1/R2 = R3/R4:
Select calculation
Top-left armEnter valid R1.
Bottom-left armEnter valid R2.
Top-right armEnter valid R3.
Bottom-right armEnter valid R4.
Bridge excitation voltageEnter valid voltage.
Series resistor Zener regulator: R = (Vin − Vz) / (Iz + IL):
Unregulated supply voltageEnter valid Vin.
Zener breakdown voltageEnter valid Vz (must be < Vin).
Maximum load current in mAEnter valid load current.
Min current to keep Zener in regulation (typical 5–10 mA)Enter valid Iz.
Zener diode power rating (common: 400, 500, 1000 mW)Enter valid power rating.
Vout
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⚠️ Disclaimer: Results use standard Ohm's Law and Thevenin's Theorem. Real circuits include component tolerances, PCB parasitic effects, and temperature variation. Always verify with measurements. Zener regulator designs should be verified with actual component datasheets.
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📚 Sources & Methodology
All voltage divider and circuit analysis formulas verified against:
IEEE Std 315-1975 (Reaffirmed 1993) — Graphic symbols and circuit definitions: Ohm's Law, Kirchhoff's Voltage Law, Thevenin's Theorem standards.ieee.org
Nilsson & Riedel, Electric Circuits (11th Ed., Pearson) — Voltage divider derivation, Thevenin equivalent, Wheatstone bridge analysis — standard undergraduate circuit theory reference pearson.com
ON Semiconductor Application Note AN920 — Zener diode voltage regulator design equations, series resistor sizing, power dissipation onsemi.com
Complete Voltage Divider Guide — Formula, Design & Applications
The Voltage Divider Formula Explained
A voltage divider uses two resistors in series to produce an output voltage between input and ground: Vout = Vin × R2 / (R1 + R2). R1 sits between Vin and Vout; R2 sits between Vout and ground. The output ratio equals the fraction of total resistance that R2 represents. Equal resistors give exactly half the input. The output can never exceed Vin and can never amplify — it only divides.
The most important limitation: a voltage divider only works well when the load resistance is much greater than R2 (at least 10×). A 10K/10K divider connected to a 10K load sees its Vout drop from Vin/2 to Vin/3 — a 33% loading error. Use the Loaded Divider mode above to calculate exact output with any load.
Voltage Divider Formulas (Ohm's Law & Thevenin's Theorem)
Basic: Vout = Vin x R2 / (R1 + R2)Find R1: R1 = R2 x (Vin - Vout) / VoutFind R2: R2 = R1 x Vout / (Vin - Vout)Thevenin: Vth = Vin x R2/(R1+R2) | Rth = R1||R2 = R1xR2/(R1+R2)Loaded: Reff = R2||RL | Vout = Vin x Reff/(R1+Reff)Wheatstone (balance): R1/R2 = R3/R4 => R4 = R3 x R2/R1Zener R: R = (Vin - Vz) / (Iz_min + IL_max)Zener P_R: P = (Vin - Vz)^2 / R
Common Voltage Divider Applications
Application
Vin
Vout
R1
R2
Notes
5V to 3.3V level shift
5V
3.30V
5.1K
10K
For ADC or UART signals
12V to 5V bias
12V
5.0V
14K
10K
Op-amp bias reference
3.3V ADC half-scale
3.3V
1.65V
10K
10K
Mid-rail reference
MCU pull-up with sensor
3.3V
variable
10K
NTC thermistor
Temperature sensing
Battery voltage monitor
12V
3.0V
27K
10K
Into 5V ADC (max 5V)
Potentiometer volume
Vs
0 to Vs
Wiper
Wiper
Variable R1 and R2
Wheatstone Bridge for Sensor Applications
The Wheatstone bridge is a precision circuit for measuring small resistance changes. Four resistors form two voltage dividers sharing the same supply. When balanced (R1/R2 = R3/R4), the differential voltage Vout = 0. Replacing one arm with a sensor (strain gauge, thermistor, RTD) causes a resistance change ΔR that produces an output voltage proportional to the change: Vout ≈ Vs × ΔR / (4R) for small changes. This high-rejection differential measurement filters out common-mode noise, supply variations, and temperature drift.
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5V to 3.3V level shifter tip: R1=15KΩ, R2=33KΩ gives Vout = 5 × 33/(15+33) = 3.44V (acceptable). Better: R1=18K, R2=33K gives 3.26V. For I2C and UART at under 100 kHz this works well. For SPI at MHz speeds, the RC time constant with line capacitance (R_eff = 11.3K for 18K||33K) limits bandwidth to about 56 kHz per 100pF line capacitance. Use a dedicated level-shifter IC (e.g., TXS0101) for high-speed signals.
❓ Frequently Asked Questions
Vout = Vin x R2 / (R1 + R2). R1 is the top resistor (between Vin and Vout), R2 is the bottom (between Vout and GND). Example: Vin=12V, R1=10K, R2=5K: Vout = 12 x 5000/15000 = 4V. The output always lies between 0 and Vin. Use the Voltage Divider tab above for instant calculation.
Choose R2 first (typically 10K for general use), then R1 = R2 x (Vin - Vout) / Vout. For 5V to 3.3V: R1 = 10000 x (5-3.3)/3.3 = 5.15K. Use 5.1K standard value. Check: Vout = 5 x 10000/15100 = 3.31V. Use the Find R1 or R2 tab above for any target voltage.
When a load RL is connected at Vout, it is in parallel with R2. Effective bottom resistance: Reff = R2||RL = R2xRL/(R2+RL). Vout_loaded = Vin x Reff/(R1+Reff). With R1=R2=10K and RL=10K: Reff = 5K, Vout = Vin x 5/15 = Vin/3 (33% lower than unloaded Vin/2). Use the Loaded Divider tab above — it calculates Thevenin equivalent and loading error automatically.
A Wheatstone bridge uses four resistors (R1, R2, R3, R4) in a diamond configuration. Balanced when R1/R2 = R3/R4. Balance condition: R4 = R3 x R2/R1. When one arm changes (sensor), the differential voltage is proportional to resistance change. Used with strain gauges, thermistors, and pressure sensors for precision measurement. The differential output rejects supply noise and common-mode interference.
R = (Vin - Vz) / (Iz_min + IL_max). Choose Iz_min = 10% of max load current. Example: Vin=12V, Vz=5.1V, IL=50mA, Iz=5mA: R = (12-5.1)/(0.05+0.005) = 125.5 ohm. Use 120 ohm. Power dissipated in R: P = (12-5.1)^2/120 = 0.40W. Use 0.5W resistor. Zener dissipation at no load: Pz = (Vin-Vz)/R x Vz = (12-5.1)/120 x 5.1 = 0.293W. Use the Zener Regulator tab above.
Vth = Vin x R2/(R1+R2) — open circuit output voltage. Rth = R1||R2 = (R1xR2)/(R1+R2) — output impedance. With load RL: Vout = Vth x RL/(Rth+RL). Example: Vin=5V, R1=15K, R2=33K: Vth = 5 x 33/48 = 3.44V, Rth = 15000x33000/48000 = 10.3K. With 100K load: Vout = 3.44 x 100000/110300 = 3.12V (9.3% drop).
For MCU ADC: 10K to 100K range minimizes current and power waste while providing low enough output impedance for ADC inputs. For level shifting: 10K/20K or 15K/33K are common. Lower values give lower output impedance (better for high-speed signals, driving loads) but waste more power. Higher values draw less current (better for battery-powered designs) but are more affected by loading. 1% resistors recommended for precision applications.
R1=15K, R2=33K: Vout = 5 x 33/48 = 3.44V (close, generally acceptable). R1=18K, R2=33K: Vout = 5 x 33/51 = 3.24V (tight). R1=56K, R2=100K: Vout = 5 x 100/156 = 3.21V (low current, for battery-powered). Output impedance of R1=15K, R2=33K: Rth = 10.3K. Acceptable for ADC inputs (typically 1M+ impedance) and UART. For fast SPI or I2C, use a dedicated level shifter IC instead.
Load RL in parallel with R2 reduces effective resistance: Reff = R2||RL, always less than R2. This shifts the ratio Reff/(R1+Reff) lower. Fix: use much lower R1/R2 values so RL >> R2 (10x minimum). Or buffer the output with a unity-gain op-amp follower — infinite input impedance, zero output impedance, exact Vth regardless of load. Use the Loaded Divider tab to quantify loading error for your specific values.
Rout = R1 || R2 = (R1 x R2)/(R1+R2). For R1=R2=10K: Rout = 5K. Any load RL forms a divider with this 5K source: Vout_loaded = Vth x RL/(5K+RL). To drive a load without voltage drop, buffer with op-amp voltage follower (Rout = milli-ohms). To keep loading under 1%: RL > 100 x R2. The Loaded Divider tab shows exact output with Thevenin analysis.
Accuracy limited by resistor tolerance and temperature coefficient. With 5% resistors: worst-case ratio error ~10%. With 1% resistors: ~2% worst case. With 0.1% resistors: ~0.2%. For precision voltage references, use 0.1% 25ppm/C resistors. Temperature drift of 100ppm/C means 0.01%/degree change. For a 50-degree range (0-50C): up to 0.5% drift with standard resistors. Use matched resistors (same batch) to reduce ratio error.
At balance (Vout=0): R4 = R3 x R2/R1. If R1=R3=1K and you adjust R2 (decade box) until bridge balances, then R4 = R2 at balance. For measurement: fix R1=R2=R3=1K, replace R4 with unknown. Adjust Vs and measure differential Vout. When Vout=0: R4=1K. If Vout≠0: use Vout=Vs x (R4/(R3+R4) - R2/(R1+R2)) to calculate R4. Use the Wheatstone Bridge tab for both balance point and differential voltage.