串联 & 并联电阻计算器
This resistor calculator computes the equivalent resistance for any number of resistors connected in series or parallel. For series circuits, the total equals the sum of all values (Rtotal = R1 + R2+ …). For parallel circuits, the total is found from the reciprocal formula (1/Rtotal = 1/R1 + 1/R2 + …). Enter your values below for an instant result.
Series & Parallel Resistor Calculator
Enter resistor values in ohms (Ω). Add or remove resistors to calculate the equivalent resistance for series or parallel configurations.
In a series circuit, resistors are connected end-to-end. The total resistance equals the sum of all individual resistances: Rtotal = R1 + R2+ …
Quick-add common values:
Equivalent Resistance (series)
600 Ω(600.00 Ω)
Resistor breakdown:
Frequently Asked Questions
串联电阻如何计算总阻值？
串联电路中，总电阻等于各电阻之和：R_total = R₁ + R₂ + R₃ + ...。串联电路中各处电流相同，总电压等于各电阻电压之和。例如，10Ω、20Ω、30Ω 串联：总阻值 = 60Ω。
并联电阻如何计算总阻值？
并联电路中，总电阻的倒数等于各电阻倒数之和：1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...。并联总阻值总小于任一支路电阻。两电阻并联时，R_total = R₁×R₂ / (R₁+R₂)。
串联和并联电路有什么实际区别？
串联电路：一个元件损坏会断开整个电路（如老式圣诞灯）；电流相同，电压按阻值比分配。并联电路：一个元件损坏不影响其他支路（如家用电路）；电压相同，电流按阻值反比分配。
如何简化复杂的串并联混合电路？
从最内层开始，逐步简化：①识别纯串联或纯并联的子网络；②计算等效电阻；③用等效电阻替代该子网络；④重复上述步骤直到简化为单一等效电阻。本计算器支持输入复杂网络并自动计算等效电阻。
Series and Parallel Resistor Guide
Series Resistor Formula
When resistors are connected in series, the same current flows through every resistor and the total (equivalent) resistance is the simple sum of all individual resistances:
Rtotal = R1 + R2 + R3 + … + Rn
For example, connecting a 100 Ω, 200 Ω, and 300 Ω resistor in series gives a total resistance of 600 Ω. The total is always larger than any individual resistor in the chain.
Series configurations naturally increase resistance. Every resistor adds to the total, so adding even a single resistor always raises the equivalent resistance.
A zero-ohm resistor (a short circuit) is valid in series — it contributes nothing to the total. A negative resistance is not physically realizable with standard passive resistors, so the calculator rejects negative values.
Parallel Resistor Formula
When resistors are connected in parallel, all resistors share the same two nodes (same voltage across each). The total equivalent resistance is found using the reciprocal formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + … + 1/Rn
The equivalent resistance of a parallel combination is always less than the smallest individual resistor. Adding more parallel paths provides more routes for current, reducing the total opposition.
For example, two 100 Ω resistors in parallel give 50 Ω — exactly half of one resistor. Three 300 Ω resistors in parallel give 100 Ω — one third of one resistor. This is a useful shortcut: n identical resistors of value R in parallel give R/n.
A zero-ohm resistor in parallel creates a short circuit (total resistance = 0 Ω). The calculator rejects zero and negative values for parallel configurations to prevent division-by-zero errors.
Two-Resistor Shortcut
For the common case of exactly two resistors in parallel, the reciprocal formula simplifies to the product-over-sum shortcut:
Rtotal = (R1 × R2) / (R1 + R2)
This is faster to compute by hand than the reciprocal formula. For instance, 100 Ω and 150 Ω in parallel:
| Product: | 100 × 150 = 15,000 |
| Sum: | 100 + 150 = 250 |
| Result: | 15,000 / 250 = 60 Ω |
For more than two resistors, apply the shortcut iteratively: combine any two resistors into their equivalent, then combine that result with the next resistor, and so on.
When to Use Each Configuration
Choosing between series and parallel depends on your circuit goals:
| Goal | Series | Parallel |
|---|---|---|
| Increase resistance | Yes — always | No — reduces it |
| Reduce resistance | No | Yes — always |
| Same current everywhere | Yes | No — current splits |
| Same voltage everywhere | No — voltage divides | Yes |
| Voltage divider | Yes | No |
| Current limiter (e.g., LED) | Yes | No |
| Load sharing / power distribution | No | Yes |
| Non-standard value from standard parts | For higher value | For lower value |
Series resistors are used to limit current (for example, a current-limiting resistor for an LED), create voltage dividers, and set bias points in amplifier circuits. Because the same current flows through every component, a failure (open circuit) in any series resistor breaks the entire path.
Parallel resistors are used when you need a lower resistance than any available standard value, or when you need to share power dissipation across multiple resistors. Because each parallel resistor is independently connected across the supply, a failure in one does not interrupt the others.
Worked Examples
Example 1: LED Current-Limiting Resistor in Series
You have a 5 V supply and want to drive a red LED (forward voltage 2.0 V, target current 20 mA). The required series resistor is:
Using two 330 Ω resistors in parallel gives 165 Ω — the closest achievable value with common 330 Ω parts. A single standard 150 Ω resistor is also readily available in the E12 series.
Example 2: Achieving a Non-Standard Value
You need exactly 750 Ω but only have 1 kΩ resistors. Connect three 1 kΩ resistors in parallel:
Two 1 kΩ in parallel = 500 Ω. One more 500 Ω (two 1 kΩ in parallel) in series = 1,000 Ω. Mix of configurations lets you build many exact values from a small set of standard parts.
Example 3: Power Distribution
A 1 kΩ resistor must dissipate 1 W across a 31.6 V source, but standard 1/4 W resistors are all you have. Place four 250 Ω resistors (two pairs of 500 Ω in parallel, then those two pairs in series) to achieve 1 kΩ total while each part only dissipates 250 mW. Alternatively, use four 1 kΩ resistors in parallel to get 250 Ω, with each sharing 250 mW — a simpler calculation.
Standard Resistor Values — E12 Series
Resistors are manufactured in standardized value series. The E12 series (12 values per decade, ~10% tolerance) is the most common in general electronics work. Multiplied by powers of 10, these 12 base values cover all decades from 1 Ω to 10 MΩ:
For example, the E12 decade starting at 100 Ω gives: 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 Ω. The next decade begins at 1.0 kΩ with the same multipliers.
When you need a value that does not appear in the E12 series, combine two standard values in series (for a value larger than either) or in parallel (for a value smaller than either). This calculator helps you verify the result instantly.