Voltage Divider Calculator Guide: Getting the Output You Want

A voltage divider is one of the simplest circuits in electronics, and also one of the most useful. Two resistors in series across a supply voltage produce a lower voltage at the junction between them. That lower voltage can feed a sensor input, set a reference level, bias a transistor, or scale a signal down to a range an analogue input can measure. The circuit uses only two components, but using it well requires understanding one formula and one important limitation.

This guide explains the formula, works through a complete example, and explains the loading problem that catches out almost everyone who uses a divider for the first time. The circuits described here are low-voltage learning circuits. Mains-powered work and high-power circuits need additional safety precautions and, where applicable, a qualified person.

The formula

Imagine a supply voltage, Vin, connected across two resistors in series: R1 on top, connected to the supply, and R2 below, connected to ground. The output voltage, Vout, is taken from the junction between R1 and R2. The same current flows through both resistors, because they are in series, so the voltage divides in proportion to the resistances. The formula is: Vout equals Vin multiplied by R2 divided by (R1 plus R2).

That formula is worth understanding rather than merely memorising. The fraction R2 divided by (R1 plus R2) is the share of the total resistance that lies below the output point, and therefore the share of the total voltage that appears at the output. If R1 and R2 are equal, the output is half the input. If R2 is much larger than R1, the output is close to the input. If R2 is much smaller than R1, the output is close to zero. The divider can only reduce a voltage, never increase it, and the output is always between zero and the input voltage.

The current through the divider is also easy to find: it is Vin divided by (R1 plus R2). That current flows continuously whenever the supply is connected, whether or not anything is using the output voltage. For a battery-powered circuit, a divider with low resistor values wastes power, while a divider with very high resistor values draws little current but becomes sensitive to loading, as explained below. Choosing resistor values is therefore a balance between power consumption and output stiffness.

A worked example

Suppose you have a 12 volt supply and you need an output of about 7 volts, for example to feed a circuit that expects a mid-range reference. Choose R1 as 2,000 ohms and R2 as 3,000 ohms. The total resistance is 5,000 ohms. The current through the divider is 12 volts divided by 5,000 ohms, which equals 0.0024 amps, or 2.4 milliamps.

The output voltage is 12 volts multiplied by 3,000 divided by 5,000, which is 12 multiplied by 0.6, giving 7.2 volts. That is close to the target of 7 volts, and it uses standard resistor values. If you needed exactly 7 volts, you could adjust the ratio: for an output of 7 volts from 12 volts, the fraction needed is 7 divided by 12, which is about 0.583. A pair such as R1 equal to 5,000 ohms and R2 equal to 7,000 ohms gives a fraction of 7,000 divided by 12,000, which is also about 0.583, and an output of 7.0 volts. In practice, the nearest standard values are usually close enough, and the exact value matters less than understanding the ratio.

Check the power in each resistor. The power in R1 is the voltage across it multiplied by the current. The voltage across R1 is the input minus the output, which is 12 minus 7.2, or 4.8 volts. Multiplying 4.8 volts by 0.0024 amps gives 0.01152 watts, or about 11.5 milliwatts. The power in R2 is 7.2 volts times 0.0024 amps, which equals 0.01728 watts, or about 17.3 milliwatts. Both are well within the rating of an ordinary quarter-watt resistor, which is the usual check to perform. At higher voltages or lower resistances, power rises quickly, so always perform this check.

A Voltage Divider Calculator does this arithmetic for any combination of input voltage and resistor values, and it can also work backwards: given a desired output voltage and one resistor value, it finds the other. That reverse calculation is often the more useful one in practice, because you usually know the output you want and need to find the resistors that produce it.

The loading problem

The formula above assumes that nothing draws current from the output. In reality, whatever you connect to the output will draw some current, and that current flows through R1 in addition to the divider current, which changes the output voltage. This is called loading, and it is the single most important limitation of a voltage divider.

Consider the example above, with an output of 7.2 volts unloaded. Suppose you connect a load that draws 2.4 milliamps, equal to the divider current. That load current must flow through R1, so the total current through R1 becomes 4.8 milliamps, while the current through R2 remains determined by the output voltage. The output voltage will fall, because R1 now drops more voltage. A precise calculation requires solving for the new output with the load in parallel with R2, but the qualitative point is enough for most purposes: if the load draws a current comparable to the divider current, the output will shift significantly.

The rule of thumb is to make the divider current at least ten times the load current, so that the load changes the output by only a small amount. If your load draws 1 milliamp, your divider should carry at least 10 milliamps, which means lower resistor values and higher power consumption. If that power cost is unacceptable, a voltage divider is the wrong tool, and you need a regulator or a buffer amplifier instead. An operational amplifier configured as a voltage follower, for example, can copy the divider voltage while supplying the load current itself, leaving the divider unloaded.

This is why dividers are excellent for setting reference voltages for high-impedance inputs, such as an analogue-to-digital converter input or a comparator input, which draw almost no current, but poor for powering a device that draws significant current. A divider can set the voltage that a sensor circuit compares against; it should not normally power the sensor itself.

Choosing resistor values

Given a desired output voltage and an acceptable divider current, you can choose resistor values systematically. First, decide the total resistance from the supply voltage and the desired current: total resistance equals Vin divided by divider current. Then, the lower resistor is the total resistance multiplied by the desired output fraction, which is Vout divided by Vin. The upper resistor is the remainder.

For example, for a 12 volt supply, a desired output of 7.2 volts, and a divider current of 2.4 milliamps, the total resistance is 12 divided by 0.0024, which equals 5,000 ohms. The lower resistor is 5,000 multiplied by 7.2 divided by 12, which is 5,000 multiplied by 0.6, giving 3,000 ohms. The upper resistor is 5,000 minus 3,000, which equals 2,000 ohms. Those are exactly the values used in the worked example, which confirms the method.

In practice, you will round to standard values, such as the E12 or E24 series, and then recalculate the output with the rounded values. Resistor tolerance, typically 5 percent for ordinary resistors or 1 percent for precision types, also shifts the output. If the output must be accurate, use 1 percent resistors, or include a small adjustable resistor, such as a trimmer potentiometer, in the divider so that the output can be set exactly and then left alone.

A potentiometer is, in fact, a variable voltage divider: a single resistive track with a wiper that divides it into two parts. Turning the knob changes the ratio and therefore the output voltage. That is why volume controls and brightness controls, which are potentiometers, behave like dividers. Understanding the fixed divider makes the variable version intuitive.

Voltage dividers appear in many places. A light-dependent resistor in series with a fixed resistor forms a divider whose output changes with light level, which is the basis of many simple light sensors. A thermistor in a divider gives an output that changes with temperature. A pair of resistors scales a 12 volt signal down to the 3.3 volt or 5 volt range that a microcontroller input can tolerate. In each case, the divider is used as a sensor interface or a signal scaler, not as a power supply, which respects the loading limitation.

The Resistor Color Code Calculator helps you identify the resistors you have fitted, and the Scientific Calculator handles the ratio arithmetic. The Transistor Bias Calculator uses a voltage divider as its first stage, and the guide for that tool explains how the divider sets a transistor's base voltage. The Transformer kVA Calculator Guide shows a different kind of electrical sizing, with the same emphasis on starting from the load and checking the result.

Safety and limits

Voltage dividers do not isolate, regulate, or protect. The output of a divider connected to a high-voltage supply is still referenced to that supply, and a fault in one resistor can expose the output to the full input voltage. Never use a resistive divider to drop mains voltage to a low voltage for powering a circuit: that is dangerous, and proper isolated power supplies exist for that purpose. For low-voltage work, keep the supply within the ratings of all components, check power dissipation, and measure the output with a multimeter before connecting it to a sensitive input.

A divider is a small circuit with a large lesson inside it: a formula is only as good as its assumptions, and the assumption here is that the output draws no current. Check that assumption for every divider you build, size the divider current to suit the load, and use a buffer or regulator when the load demands it. With that discipline, two resistors and one formula will serve you reliably across a wide range of projects.