A divider uses series voltage drops
A voltage divider places two resistors in series across an input voltage and takes the output from their junction. The same current flows through both unloaded resistors, so each voltage drop is proportional to resistance.
With R₁ on top and R₂ connected to the reference node, the ideal unloaded output is:
Vout = Vin × R₂ ÷ (R₁ + R₂)
This simple relationship is widely used for sensing, biasing, reference scaling, and level reduction. It does not create a stiff power supply.
Deriving the formula
The series current follows Ohm’s law:
I = Vin ÷ (R₁ + R₂)
Output voltage is the drop across R₂:
Vout = I × R₂
Substitute the current expression:
Vout = Vin × R₂ ÷ (R₁ + R₂)
If both resistors are equal, output is half the input. If R₂ is three times R₁, output is three quarters of input. The ratio matters for the ideal unloaded voltage.
A loaded divider
Real outputs connect to something: a meter, ADC input, amplifier, transistor, or another network. Its input resistance appears in parallel with R₂.
Rlower = R₂ × Rload ÷ (R₂ + Rload)
Vout = Vin × Rlower ÷ (R₁ + Rlower)
Parallel resistance is always lower than either branch. The loaded output is therefore lower than the unloaded value for positive resistances.
The calculator applies this model when a load is entered and reports both loaded and unloaded outputs so the loading error is visible.
Worked unloaded example
An input of 12 V is connected across two 10 kΩ resistors.
I = 12 ÷ 20,000 = 0.0006 A = 0.6 mA
Vout = 0.6 mA × 10 kΩ = 6 V
Power in each resistor is I²R = 3.6 mW. The divider continuously draws 7.2 mW from the source even when nothing uses the output.
Equal resistance produces a 50% ratio, but tolerance and source conditions affect the measured value.
Worked loaded example
Connect a 10 kΩ load to the same 10 kΩ lower resistor. Their parallel combination is 5 kΩ.
Rlower = 10 kΩ || 10 kΩ = 5 kΩ
Vout = 12 × 5 ÷ (10 + 5) = 4 V
The unloaded prediction was 6 V, so the load caused a 2 V error. The divider was not capable of maintaining the expected voltage into a load equal to R₂.
Increasing load resistance to 1 MΩ makes the effective lower resistance approximately 9.901 kΩ and output about 5.970 V, much closer to ideal.
Thevenin equivalent
Seen from its output, an ideal divider can be replaced by a Thevenin voltage source and resistance:
Vth = Vin × R₂ ÷ (R₁ + R₂)
Rth = R₁ || R₂
The load and Rth then form another divider. This view makes loading intuitive: accuracy improves when Rload is much larger than Rth.
For equal 10 kΩ resistors, Rth is 5 kΩ. A 1 MΩ load is 200 times larger and causes modest static loading. A 10 kΩ load is only twice Rth and causes a large change.
Choosing the ratio
For a desired unloaded ratio k = Vout/Vin:
k = R₂ ÷ (R₁ + R₂)
R₁/R₂ = (1 − k) ÷ k
To reduce 12 V to 3 V, k is 0.25, so R₁ should be three times R₂. Values such as 30 kΩ and 10 kΩ give the ideal ratio.
Available standard resistor series and tolerance determine the actual choice. A pair can be scaled up or down while preserving the ideal ratio, but absolute values change other performance.
Low resistance versus high resistance
Lower resistor values draw more current and dissipate more power. They also create a lower output resistance, making the divider less sensitive to a given load current, leakage, contamination, and some noise sources.
Higher values save power but create a weaker output. Input bias current, ADC sampling current, PCB surface leakage, meter impedance, and parasitic capacitance can cause greater error or slower settling.
There is no universally best range. Battery devices often prioritise power; fast data acquisition may require low source impedance or a buffer. Component voltage rating and available resistor values also matter.
Resistor tolerance
The output depends on a ratio, so the tolerances of both resistors matter. Two nominal 1% resistors can move in opposite directions and create a ratio error larger than one percent of output.
Worst-case analysis evaluates the combinations that maximize and minimize the ratio. Statistical analysis can be appropriate for production distributions when assumptions are justified.
Matched resistor networks can provide better ratio tracking than unrelated discrete parts even when their absolute resistance tolerance is similar.
Temperature coefficients also matter when R₁ and R₂ heat differently or use different technologies.
Power dissipation
The unloaded series current is Vin/(R₁+R₂). Individual resistor powers are:
P₁ = I²R₁
P₂ = I²R₂
With a load, current through R₁ splits between R₂ and the load. The calculator separately reports R₁ and R₂ power using the loaded output.
Check steady-state and transient voltage, power rating, pulse capability, ambient temperature, and manufacturer derating. High-voltage dividers may need several series resistors to meet working-voltage limits even when total power is low.
ADC inputs
Dividers commonly scale a voltage into an analog-to-digital converter range. The ADC input is not always a simple fixed resistance. Sample-and-hold capacitors draw pulses of charge and need time to settle through source impedance.
Datasheets often state a maximum recommended source resistance, acquisition time, input leakage, and protection limits. A capacitor across R₂ can reduce high-frequency impedance and noise but changes response time and startup behaviour.
Never assume the divider alone protects an input from transients, negative voltage, or power-off conditions. Use the manufacturer’s interface guidance.
Dividers are not voltage regulators
A divider output changes when load current changes. It also changes directly with input voltage. This makes it unsuitable as a general power source.
Linear regulators, switching converters, reference ICs, and buffer amplifiers are designed to maintain output across a specified load and input range. They include their own stability, dropout, thermal, and protection requirements.
A divider can set a regulator feedback ratio or provide a sensing signal because those inputs draw controlled small currents. It should not replace the regulator.
Meter loading
Measuring the divider adds the meter’s input resistance as another load. A common digital multimeter may have input resistance around a stated value, but the exact value and mode belong to the instrument specification.
On a low-resistance divider the effect can be negligible. On a multi-megohm divider it can dominate and make the reading lower than the voltage that existed before connection.
Include meter resistance as the load when predicting this effect.
AC and frequency response
The simple formula assumes resistive elements and negligible parasitic effects. At changing signals, capacitance from wiring, devices, and the load combines with divider resistance to form frequency-dependent behaviour.
A general impedance divider uses:
Vout = Vin × Z₂ ÷ (Z₁ + Z₂)
Z can be complex and frequency dependent, so output has magnitude and phase. Oscilloscope probes deliberately use compensated dividers to maintain ratio across frequency.
This calculator handles real resistances only.
Safety and high voltage
A mathematically correct divider can still be unsafe. High voltage design requires resistor working-voltage ratings, creepage, clearance, insulation, pollution degree, transient category, fault analysis, and safe discharge paths.
Open-circuit failures can expose a low-voltage output to dangerous voltage. Stored charge can remain after power is removed. Measurement equipment needs suitable category and voltage ratings.
Do not use a browser calculation as a high-voltage design approval.
Limits of this calculator
The tool models an ideal DC source, two positive resistors, and an optional purely resistive load. It reports static output, currents, effective resistance, and resistor power.
It does not include source resistance, tolerance, temperature, input bias current, sampling dynamics, capacitance, inductance, noise, transients, component voltage ratings, or faults.
Use it to establish the nominal relationship and quantify simple loading. Use component datasheets, worst-case analysis, simulation, measurement, and applicable safety standards for real hardware.