Engineering · Electrical Engineering · Circuit Analysis
Voltage Divider Calculator
Calculates the output voltage across a resistor in a series voltage divider circuit given input voltage and two resistor values.
Calculator
Formula
V_{out} is the output voltage measured across R2 (in volts). V_{in} is the input voltage applied across both resistors in series (in volts). R_1 is the upper resistor (in ohms) connected between V_{in} and the output node. R_2 is the lower resistor (in ohms) connected between the output node and ground. The ratio R_2 / (R_1 + R_2) is the divider ratio, always between 0 and 1, ensuring V_{out} is always less than or equal to V_{in}.
Source: Ohm's Law and Kirchhoff's Voltage Law — Alexander & Sadiku, Fundamentals of Electric Circuits, 6th Edition, McGraw-Hill.
How it works
A voltage divider consists of two resistors, R1 and R2, connected in series across a supply voltage Vin. The output voltage Vout is taken at the junction between the two resistors — effectively the node between R1 and R2 — and measured relative to ground. Because both resistors carry the same current (they are in series and no current is drawn from the output node in the ideal case), the voltage drops are proportional to each resistor's value relative to the total resistance.
The governing formula is derived directly from Ohm's Law and Kirchhoff's Voltage Law: Vout = Vin × R2 / (R1 + R2). The divider ratio R2 / (R1 + R2) is always between 0 and 1, which means the output voltage is always less than or equal to the input voltage. Increasing R2 relative to R1 raises Vout closer to Vin; increasing R1 relative to R2 pulls Vout closer to ground. The series current through both resistors is I = Vin / (R1 + R2), and power dissipated in each resistor can be calculated from P = I² × R.
Voltage dividers appear throughout practical electronics: setting the non-inverting input of an op-amp, biasing the base of a BJT transistor, scaling a high-voltage signal to within the range of an analog-to-digital converter (ADC), forming a Wheatstone bridge with resistive sensors, and creating logic-level shifters. They are equally common in precision measurement systems, audio attenuators, and power supply feedback networks. The simplicity and reliability of the divider make it indispensable in circuit design.
Worked example
Suppose you have a 12 V supply and need to produce a 4.4 V reference for a sensor input. You choose R1 = 10 kΩ and R2 = 4.7 kΩ.
Step 1 — Total resistance: Rtotal = R1 + R2 = 10,000 + 4,700 = 14,700 Ω
Step 2 — Divider ratio: Ratio = R2 / Rtotal = 4,700 / 14,700 ≈ 0.31973
Step 3 — Output voltage: Vout = 12 × 0.31973 ≈ 3.837 V
Step 4 — Series current: I = 12 / 14,700 ≈ 0.000816 A (816 µA)
Step 5 — Power in R1: PR1 = (816 µA)² × 10,000 ≈ 6.66 mW
Step 6 — Power in R2: PR2 = (816 µA)² × 4,700 ≈ 3.13 mW
Total power dissipation is about 9.8 mW, well within the power rating of standard ¼ W resistors. If the target was precisely 4.4 V, you would adjust R2 to approximately 5.87 kΩ (using R2 = Vout × R1 / (Vin − Vout) = 4.4 × 10,000 / 7.6).
Limitations & notes
The ideal voltage divider formula assumes that no current is drawn from the output node — that is, the load impedance connected to Vout is infinite. In practice, any load resistor RL connected in parallel with R2 lowers the effective lower resistance, pulling Vout below the unloaded value. As a rule of thumb, the load resistance should be at least 10 times greater than R2 to keep the loading error below approximately 10%. For precision applications, a buffer amplifier (voltage follower) should be placed between the divider output and the load to eliminate loading effects entirely. Additionally, resistors have tolerances (typically 1% or 5%), which directly affect Vout accuracy; for tight voltage references, precision resistors or a dedicated reference IC should be used instead. The formula also does not account for temperature coefficients of resistance, parasitic capacitance at high frequencies, or noise introduced by resistors (Johnson–Nyquist noise), all of which become important in RF, high-speed digital, and low-noise analog designs.
Frequently asked questions
What is the voltage divider rule?
The voltage divider rule states that the voltage across any resistor in a series circuit is equal to the total supply voltage multiplied by the ratio of that resistor's value to the total series resistance. For two resistors R1 and R2, the voltage across R2 is V_in × R2 / (R1 + R2). This follows directly from Ohm's Law applied to series resistors.
Can a voltage divider increase voltage above Vin?
No. A passive resistive voltage divider can only attenuate voltage — V_out is always less than or equal to V_in because the divider ratio R2 / (R1 + R2) is always between 0 and 1. To boost voltage above the supply, you need an active circuit such as a boost converter or an amplifier.
How do I choose R1 and R2 for a target output voltage?
Rearrange the formula to find the required ratio: R2 / R1 = V_out / (V_in − V_out). Choose a convenient value for one resistor, then calculate the other. For example, if V_in = 5 V and you want V_out = 3.3 V, the ratio R2/R1 = 3.3 / 1.7 ≈ 1.94. With R1 = 10 kΩ, R2 ≈ 19.4 kΩ (use the nearest standard value such as 20 kΩ).
Why does connecting a load change the output voltage?
When a load is connected across R2, it appears in parallel with R2, reducing the effective lower resistance of the divider. This lowers the divider ratio and therefore reduces V_out below the unloaded value. The effect is significant when the load resistance is comparable to R2; to minimise loading, make R2 much smaller than the load impedance, or use a buffer amplifier after the divider.
Is a voltage divider suitable as a power supply?
Generally no. A resistive voltage divider is only appropriate for low-current signal applications. Because the divider continuously draws quiescent current even with no load, it wastes power. Under a varying load, the output voltage shifts significantly. For a stable, regulated power supply, use a linear voltage regulator (such as an LM7805) or a switching regulator instead.
Last updated: 2025-01-15 · Formula verified against primary sources.