Formula and Method for the Voltage Divider
A voltage divider is two resistors, R1 and R2, connected in series across a voltage source Vin. The output, Vout, is tapped from the node between them, and it is always a fraction of Vin set by the resistor ratio: Vout = Vin × R2 / (R1 + R2). This calculator also reports the current through the divider and the power each resistor dissipates, and it can factor in a load resistor connected to the output.
Deriving the voltage divider formula
With no load connected, R1 and R2 form a single series loop, so the same current I flows through both: I = Vin / (R1 + R2), by Ohm's law applied to the total resistance. The output voltage is simply that current times R2: Vout = I × R2 = Vin × R2 / (R1 + R2). Notice Vout depends only on the ratio R2 / (R1 + R2), not on the absolute resistor sizes — 1 kΩ and 1 kΩ give the same 50% division as 100 kΩ and 100 kΩ, though the current and power differ enormously between the two.
Accounting for a load resistor
A real circuit connected to Vout draws its own current, which is electrically the same as placing a load resistor RL in parallel with R2. The pair combines to an effective resistance R2' = (R2 × RL) / (R2 + RL), which is always smaller than R2 alone, so the loaded output voltage Vin × R2' / (R1 + R2') is always lower than the unloaded value. This calculator's optional "Load Resistance" field applies that correction automatically — leave it blank to see the ideal, unloaded divider. As a design rule, keeping RL at least 10 times R2 limits the loading error to roughly 1% or less.
Choosing resistor values and power ratings
- Lower resistances (hundreds of ohms to a few kΩ) draw more current and are more resistant to loading effects, but they dissipate more power as heat and draw more current from the source.
- Higher resistances (tens of kΩ to MΩ) save power and current but make the divider more sensitive to loading and to any input bias current drawn by whatever reads Vout.
- Power rating: each resistor must be rated above its calculated power dissipation (P = I² × R), typically with a safety margin of 2× or more for reliability.
Frequently Asked Questions
What is the voltage divider formula?
How does a load resistor change the output voltage?
How do I choose resistor values for a voltage divider?
How much power does a voltage divider dissipate?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
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General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |