Circuit Analysis calculator
Series Resistor Calculator
This series resistor calculator adds total resistance, loop current, voltage drops, and resistor power for one resistor string. A 12V source with 100, 220, and 330 ohms totals 650 ohms, so the loop current is 18.46 mA and each drop stays proportional to its resistor value.
Updated October 29, 2026
100Ω + 220Ω + 330Ω in series totals 650Ω; on 12V the loop current is 18.46 mA and every resistor carries that same current.
I = V / Rtotal | 12V / 650Ω = 18.46 mA | Voltage drops follow each resistor value
Enter two to five resistor values and an optional source voltage to solve total resistance, loop current, voltage drops, and watts
Example Calculations
How to Use
Series Resistor Formula Quick Reference
| Parameter | Formula | Example |
|---|---|---|
| Total Resistance | Rtotal = R₁ + R₂ + R₃ + ... | 100Ω + 220Ω + 330Ω = 650Ω |
| Current (same all) | I = Vtotal/Rtotal | I = 12V/650Ω = 18.5mA |
| Voltage Drop | Vn = I × Rn | V₁ = 18.5mA × 100Ω = 1.85V |
| Voltage Divider (2R) | Vout = Vin × R₂/(R₁+R₂) | Vout = 12V × 220/(100+220) = 8.25V |
| Power per Resistor | Pn = I² × Rn | P = 18.5mA² × 100Ω = 34.2mW |
| Total Power | Ptotal = I² × Rtotal = V²/Rtotal | P = 18.5mA² × 650Ω = 222mW |
Key Principles (Kirchhoff's Voltage Law)
- Rtotal > Rmax: Series resistance is always greater than any individual resistor
- Same Current: All series resistors carry identical current (I₁ = I₂ = I₃...)
- Voltage Sum: Total voltage equals sum of voltage drops (Vtotal = V₁ + V₂ + V₃...)
- Proportional Voltage Division: Higher resistance → Higher voltage drop (V ∝ R)
- Power Distribution: Higher resistance → Higher power dissipation (P ∝ R)
Calculation Instructions
Enter resistance values in ohms (Ω), kilohms (kΩ), or megohms (MΩ). Specify applied voltage to calculate current, individual voltage drops, and power dissipation. Calculator determines: (1) Total series resistance, (2) Circuit current, (3) Voltage drop across each resistor, (4) Power dissipation per resistor. For voltage divider design, use ratio: Vout/Vin = R₂/(R₁+R₂).
Series vs. Parallel Resistor Comparison
| Parameter | Series Configuration | Parallel Configuration |
|---|---|---|
| Equivalent R | Req = R₁ + R₂ (Req > Rmax) | 1/Req = 1/R₁ + 1/R₂ (Req < Rmin) |
| Current | Same through all (I₁ = I₂ = Itotal) | Divides (Itotal = I₁ + I₂) |
| Voltage | Divides (Vtotal = V₁ + V₂) | Same across all (V₁ = V₂ = Vtotal) |
| Example (100Ω, 200Ω) | Req = 300Ω (higher than 200Ω) | Req = 66.7Ω (lower than 100Ω) |
| Primary Use | Voltage division, higher resistance | Current division, lower resistance |
Standard E12/E24 Resistor Series for Series Combinations
| Series | Tolerance | Standard Values (Ω) |
|---|---|---|
| E12 | ±10% | 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 (×10n) |
| E24 | ±5% | 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91 |
Common Series Combinations: 100Ω + 220Ω = 320Ω, 1kΩ + 2.2kΩ = 3.2kΩ, 10kΩ + 10kΩ = 20kΩ. For voltage dividers, choose ratios for the desired output: 1kΩ + 2kΩ gives 2/3 voltage division (67%). Confirm the actual tolerance and temperature coefficient from the selected component documentation when ratio accuracy matters.
When a series string is a voltage divider
A series-resistor string can provide a divider ratio when the output is taken across one resistor. This calculator reports the nominal drops from the supplied resistor values and supply voltage; it does not accept a downstream load-current or load-resistance field. Use the Voltage Divider Calculator when you need a target Vout, standard resistor selection, or a loaded-output estimate.
Understanding Series Resistor Circuits and Applications
Series resistor circuits form the foundation of voltage divider networks, bias circuits, and current limiting applications in electronic systems. When resistors are connected in series, they share the same current while voltage divides proportionally across each component based on its resistance value. This fundamental principle enables precise voltage reference generation, signal conditioning, and load matching in analog and digital circuits.
For a full walkthrough of series versus parallel behavior and worked DC examples, see the Series and Parallel Circuits guide. Use this calculator for numerical checks on specific resistor strings, then refer to the guide to verify assumptions, edge cases, and analysis steps.
This calculator supports 2–20 resistors in one series string. Use it to verify the total resistance, common current, individual voltage drops, power, and tolerance range before checking component ratings in the surrounding circuit.
Practical Engineering Considerations
| Consideration | Impact | Best Practice |
|---|---|---|
| Tolerance Stack-Up | ±10% resistors in series: 100Ω±10Ω + 200Ω±20Ω = 300Ω±30Ω (still ±10% worst-case) | Use ±1% (E96) or ±5% (E24) for precision. Worst-case: ΔRtotal = ΔR₁ + ΔR₂. RSS method: √(ΔR₁² + ΔR₂²) for statistical analysis. |
| Power Derating | Each resistor must handle P = I²×R individually | Follow the component manufacturer's derating curve and verify dissipation at the expected ambient temperature; there is no universal derating percentage. |
| Temperature Coefficient | Resistance changes with the component temperature coefficient and the temperature range | Use the selected component's datasheet values. Match temperature behavior when divider-ratio stability matters: ΔVout/Vout depends on the difference between the two coefficients over the temperature change. |
| Loaded divider | A downstream load changes the divider result | Use the Voltage Divider Calculator, which accepts load current in mA, for that separate check. |
| Model boundary | The calculator is a resistor-string DC screen | For reactive or frequency-dependent behavior, use a circuit-analysis or RC calculator with the relevant inputs. |
Use the result modes for the task at hand: total resistance checks the sum of a 2–20 resistor string; voltage division adds a supply voltage and reports the common current and each drop; power analysis reports total and per-resistor dissipation; tolerance analysis reports the nominal, minimum, maximum, and RSS estimate from the selected tolerance.
For a full topology explanation, see the Series and Parallel Circuits guide. Use Parallel Resistor Calculator for a parallel component network and Ohm's Law Calculator when the task is a single V-I-R relationship.
Common Applications
Frequently Asked Questions
How do I calculate total resistance for series resistors?
For series resistors, simply add all resistance values: Rtotal = R1 + R2 + R3 + ... For example, 100Ω, 200Ω, and 300Ω in series equals 600Ω total. The total resistance is always greater than any individual resistor value, and the same current flows through all resistors.
How does voltage divide across series resistors?
Voltage divides proportionally to resistance values. For each resistor: V = (R/Rtotal) × Vtotal. Higher resistance values get larger voltage drops. For example, in a 12V circuit with 100Ω and 200Ω resistors: V1 = (100/300) × 12V = 4V, V2 = (200/300) × 12V = 8V.
How do I design a voltage divider using series resistors?
Choose resistor ratios to achieve desired output voltage: Vout = Vin × (R2/(R1 + R2)) for a two-resistor divider. For precision applications, consider load effects, temperature coefficients, and use precision resistors. Higher total resistance reduces current but may increase noise susceptibility.
What are common design errors with series resistors and how do I avoid them?
Common errors are entering fewer resistor values than the selected count, omitting the supply voltage for voltage or power analysis, confusing component voltage drop with wire voltage drop, and overlooking per-resistor power or tolerance. Use the result mode that matches the question, then verify the component ratings and any downstream load separately.
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