Series/Parallel Resistor Calculator
On this page
Calculate
Series chains resistors end-to-end (same current through all). Parallel connects resistors between the same two nodes (same voltage across all).
Number of resistors in the network (2–20). Shows the corresponding value fields.
Resistor 1 value. Required.
Resistor 2 value. Required.
Applied to each resistor that has no individual tolerance override. Default is 5% commercial grade.
E-series for standard-value matching per IEC 60063. E24 is most common for general-purpose design.
Individual tolerance overrides, power ratings, applied V/I (all optional — leave empty if not needed).
Overview
This calculator computes the equivalent resistance of 2 to 20 resistors connected in series or parallel, matches the result to the nearest standard E-series value per IEC 60063 (E12, E24, E48, E96, or E192), propagates component tolerances to the equivalent network tolerance using both worst-case linear and RSS statistical estimates, and evaluates per-resistor power dissipation whenever applied voltage or current is specified.
Power calculation runs independently of whether resistor power ratings are provided. Per-resistor dissipation P_i is computed whenever applied V or I is specified, with explicit transparency when ratings are absent. This separation prevents the common misleading impression that absence of power values means safe operation, and lets the engineer compare computed P_i to typical SMT package ratings before specifying rating in procurement.
Two-track status classification. Track A — Power Adequacy — classifies the network as ADEQUATE (utilization ≤ 50%), AT-LIMIT (50% to 100%), or OVERLOAD (above 100%) against the 50% derating engineering-practice threshold when power ratings are specified. Track B — E-Series Match — classifies the equivalent resistance as EXACT, NEAR, or CUSTOM against the target IEC 60063 series. Combined badge shows both when both tracks are active (e.g., ADEQUATE / EXACT); OVERLOAD takes headline priority and suppresses Track B.
Tolerance propagation shows both worst-case linear sum (conservative bound — appropriate for low-volume or critical applications) and RSS statistical estimate (realistic bound for high-volume production assuming independent normal distribution of component errors), always shown simultaneously so the engineer chooses the appropriate estimate for the production context.
How to Use This Calculator
Select topology — Series or Parallel.
Set Resistor Count (2–20) — dynamically shows the corresponding R value fields.
Enter R1 and R2 with inline value and unit (Ω, kΩ, or MΩ). These are required.
Add R3–R_N as needed — enter the value and unit for each additional resistor in the count. Leave empty to exclude.
Set default tolerance (applies to all resistors without individual override). Default is 5% commercial grade.
Select target E-series for standard-value matching. Default is E24.
Click Calculate for basic result, or open Show advanced parameters to enter individual tolerance overrides, power ratings, and applied V/I.
Click Calculate — the equivalent resistance, E-series match, tolerance, power dissipation, and status badge appear in Results.
R1 and R2 are required. R3–R20 are optional — set Resistor Count to include them, leave value empty to exclude. Per-resistor tolerance of 0% is treated as 'use default'. Power adequacy classification requires both applied V or I AND at least one power rating. If only V or I is provided without ratings, power is calculated and displayed but adequacy is not classified.
Inputs & Outputs
Inputs
Required inputs
- •Topology — Series (same current through all resistors) or Parallel (same voltage across all resistors)
- •Resistor Count — 2–20, integer — dynamically shows the corresponding value fields
- •Resistor values (R1 through R_N) — Each value entered with inline unit selector (Ω / kΩ / MΩ). R1 and R2 are required minimum; R3 through R_N appear only when Resistor Count includes them
Defaultable inputs
- •Default Tolerance — 1% / 2% / 5% / 10% / 20% — applied to all resistors without individual override. Default: 5% commercial grade
- •Target E-Series — E12 / E24 / E48 / E96 / E192 — for E-series match classification. Default: E24
Optional advanced inputs (Show advanced parameters)
- •Per-resistor tolerance overrides (R1 through R_N) — 0% to 50% per resistor. Empty value applies the default tolerance
- •Per-resistor power ratings (R1 through R_N) — In watts. Enables power adequacy classification (ADEQUATE / AT-LIMIT / OVERLOAD) when applied V or I is also provided
- •Applied Voltage — V — enables per-resistor power dissipation calculation. Optional
- •Applied Current — A — alternative to Applied Voltage. If both are entered and inconsistent with calculated R_eq, voltage is used as the primary source of truth
Outputs
Always shown (when calculation valid)
- •Equivalent Resistance R_eq — With smart-display unit (Ω, kΩ, or MΩ per magnitude)
- •Nearest E-Series Value — Matched to the selected target E-series per IEC 60063
- •E-Series Deviation — Signed percent deviation from nearest standard value
- •Tolerance Worst-Case — Conservative bound — linear sum of individual contributions
- •Tolerance RSS Statistical — Realistic bound — root-sum-square of contributions for high-volume production
- •Status badge — Combined Track A / Track B classification (e.g., ADEQUATE / EXACT, OVERLOAD, NEAR)
Shown when applied V or I is provided
- •Total Power Dissipation — W or mW per smart display
- •Network Current — mA or A per smart display
- •Network Voltage — V
- •Per-Resistor Table — Columns: index, value, tolerance, V_i, I_i, P_i, rating, utilization. Rating and utilization columns show — for resistors without specified ratings
Shown when relevant
- •Dominant resistance contributor — Which resistor accounts for the largest share of R_eq (suppressed in balanced networks where spread is < 5 percentage points)
- •Dominant tolerance contributor — Which resistor accounts for the largest share of ΔR_eq (shown only when different from dominant resistance contributor)
- •Recommended adjustments — For OVERLOAD: recommended voltage reduction and next-higher power rating. For AT-LIMIT: recommended power rating upsizing
Formula
Calculator Formula
Stage 1 — Equivalent Resistance
Series: R_eq = R1 + R2 + R3 + ... + Rn = Σ(Ri)
Parallel: 1/R_eq = 1/R1 + 1/R2 + ... + 1/Rn → R_eq = 1 / Σ(1/Ri)
For 2 resistors in parallel: R_eq = (R1 × R2) / (R1 + R2)
Stage 2 — Tolerance Propagation
For each resistor, ΔRi = Ri × tol_i (where tol_i is the tolerance fraction).
Worst-case (conservative — for low-volume or critical applications):
- Series: tol_eq_wc = Σ(Ri × tol_i) / R_eq (weighted average by resistance share)
- Parallel: tol_eq_wc = Σ((R_eq / Ri) × tol_i) (weighted by conductance share)
RSS statistical (realistic — for high-volume production with independent normal distribution):
- Series: tol_eq_rss = √(Σ((Ri × tol_i)²)) / R_eq
- Parallel: tol_eq_rss = √(Σ((R_eq / Ri × tol_i)²))
Worst-case and RSS do NOT coincide even when all individual tolerances are equal. For N identical resistors in series at tol, worst-case = tol and RSS = tol / √N.
Stage 3 — E-Series Matching (IEC 60063)
- Determine decade: decade = floor(log10(R_eq))
- Compute mantissa: m = R_eq / 10^decade
- Find nearest E-series mantissa by minimizing |m − E_candidate|
- E_nearest = nearest_mantissa × 10^decade
- deviation = (R_eq − E_nearest) / E_nearest × 100 (%)
Classification:
- EXACT: |deviation| < 0.1% (true nominal match)
- NEAR: 0.1% ≤ |deviation| ≤ E-series nominal tolerance
- CUSTOM: |deviation| > E-series nominal tolerance
E-series nominal tolerance: E12=10%, E24=5%, E48=2%, E96=1%, E192=0.5%
Stage 4 — Power Dissipation (when applied V or I provided)
Series — same current through all: I_total = V_applied / R_eq (if V applied) or I_applied (if I applied) P_i = I_total² × Ri
Parallel — same voltage across all: V_total = V_applied (if V applied) or I_applied × R_eq (if I applied) P_i = V_total² / Ri
Stage 5 — Power Adequacy (Track A, when ratings provided)
util_i = P_i / rating_i max_util = max(util_i) across rated resistors only
| Class | Condition |
|---|---|
| OVERLOAD | max_util > 1.0 |
| AT-LIMIT | 0.5 < max_util ≤ 1.0 |
| ADEQUATE | max_util ≤ 0.5 |
Stage 6 — Combined Status Badge
Track B (E-series match) always shown. Track A (power adequacy) shown only when V or I AND ratings are provided. OVERLOAD suppresses Track B in the combined badge.
What Is a Series/Parallel Resistor Calculation
Series and parallel resistor combinations are the fundamental configurations of resistive circuit design. Series connection chains resistors end-to-end so the same current flows through each; the equivalent resistance is the sum of individual resistances, and voltage divides across them in proportion to each resistance. Parallel connection branches resistors between the same two nodes so the same voltage appears across each; the equivalent resistance is the reciprocal of the sum of conductances, and current divides through them in inverse proportion to each resistance.
The two configurations have opposite behaviors. Adding a resistor in series always increases the equivalent resistance — the result is larger than any individual resistor in the chain. Adding a resistor in parallel always decreases the equivalent resistance — the result is smaller than any individual resistor in the network. Series configurations are used for current limiting, voltage division, and impedance matching. Parallel configurations are used for current sharing, equivalent resistance reduction below the smallest available standard value, tolerance averaging, and parallel power distribution.
The E-series standard catalog (IEC 60063) provides a finite set of preferred resistance values per decade. When a precise non-standard resistance is required, engineers combine standard resistors in series or parallel to approximate the target value. The practical questions are: what is the equivalent resistance of the chosen combination, and is the equivalent close enough to a standard catalog value that a single resistor could replace the combination?
Tolerance propagation is the third dimension of resistor network design. Individual component tolerances combine into an equivalent network tolerance that depends on both the topology (series vs parallel) and the relative contribution of each resistor to the equivalent. The worst-case linear sum is the conservative bound; the RSS statistical estimate is the realistic bound for high-volume production assuming independent normal distribution.
Resistors in Series Formula
Series connection chains resistors end-to-end so the same current flows through each. The equivalent resistance is the simple sum:
R_eq = R1 + R2 + R3 + ... + Rn = Σ(Ri)
Voltage divides across the chain in proportion to each resistance: V_i = (Ri / R_eq) × V_total. The largest resistor in the chain drops the most voltage and dissipates the most power. Adding any resistor in series always increases the equivalent resistance — the result is always larger than any individual resistor in the chain.
Resistors in Parallel Formula
Parallel connection branches resistors between the same two nodes so the same voltage appears across each. The equivalent resistance is the reciprocal of the sum of conductances:
1 / R_eq = 1/R1 + 1/R2 + ... + 1/Rn → R_eq = 1 / Σ(1/Ri)
For 2 resistors in parallel: R_eq = (R1 × R2) / (R1 + R2). For 2 equal resistors: R_eq = R / 2. For N equal resistors: R_eq = R / N.
Current divides through the branches in inverse proportion to each resistance: I_i = (R_eq / Ri) × I_total. The smallest resistor carries the most current and dissipates the most power. Adding any resistor in parallel always decreases the equivalent resistance.
How to Find the Nearest Standard Resistor Value
E-series matching identifies the standard catalog resistor closest to the calculated equivalent. The procedure:
- Determine the decade: decade = floor(log10(R_eq)). For R_eq = 1500 Ω, decade = 3 (search 1000–9999 range). For R_eq = 500 Ω, decade = 2 (search 100–999 range).
- Search the target E-series within that decade for the value nearest to R_eq by minimizing |R_eq − E_candidate|.
- Compute deviation = (R_eq − E_nearest) / E_nearest × 100, preserving sign.
- Classify: EXACT if |deviation| < 0.1%; NEAR if 0.1% ≤ |deviation| ≤ E-series nominal tolerance; CUSTOM if |deviation| > nominal tolerance.
E-series nominal tolerance: E12 = 10%, E24 = 5%, E48 = 2%, E96 = 1%, E192 = 0.5%.
Worst-Case vs RSS Tolerance
Worst-case linear sum assumes all resistors deviate to their maximum tolerance limits in the same direction simultaneously. For each resistor ΔRi = Ri × tol_i. The worst-case network tolerance is the weighted sum of individual deviations.
RSS (Root Sum of Squares) statistical estimate assumes individual tolerances are independent and normally distributed. The combination uses root-sum-square, which is always less than worst-case for more than one resistor.
Important: worst-case and RSS do NOT coincide even when all individual tolerances are equal. For series with N identical resistors each at tol, worst-case = tol and RSS = tol / √N. Two equal 5% resistors in series: worst-case 5%, RSS 3.54%. Four equal: worst-case 5%, RSS 2.5%. The divergence is largest for balanced networks and shrinks when one resistor dominates.
Key Facts
- For N equal resistors in parallel, R_eq = R / N. Two 1 kΩ resistors in parallel give 500 Ω; four give 250 Ω.
- Worst-case and RSS tolerance propagation do NOT coincide even when all tolerances are equal. For two 5% resistors in series, worst-case is 5% and RSS is 3.54% (= 5% / √2).
- The E-series (IEC 60063) provides preferred resistance values per decade: E12 (12 values, 10% grade), E24 (24 values, 5% grade), E48 (48 values, 2% grade), E96 (96 values, 1% grade), E192 (192 values, 0.5% grade).
- E24 values at 1% procurement tolerance are readily available in modern catalogs — the E-series family defines the value set, not the procurement tolerance.
- In a series network, the resistor with the largest resistance dissipates the most power (P = I² × R with the same I through all).
- In a parallel network, the resistor with the smallest resistance dissipates the most power (P = V² / R with the same V across all).
- Engineering practice recommends 50% derating from rated power for resistor reliability — a 0.25 W rated resistor should dissipate no more than 0.125 W continuously.
- Standard SMT package power ratings: 0402 = 0.063 W, 0603 = 0.10 W, 0805 = 0.125 W, 1206 = 0.25 W, 2010 = 0.50 W, 2512 = 1.0 W.
- The dominant contributor to equivalent resistance and the dominant contributor to equivalent tolerance can be different resistors when tolerance grades vary across the network.
Applications
- Procurement optimization — identifying when a non-standard R_eq can be replaced by a single E24 or E96 catalog resistor within tolerance.
- Precision voltage divider design — verifying equivalent resistance of divider arms and tolerance propagation for instrumentation amplifier and reference networks.
- Current-limiting resistor combinations — series pairs for LED drivers and indicator circuits where a single standard value doesn't exist.
- Parallel power distribution — paralleling two resistors to distribute heat dissipation when a single higher-wattage part is unavailable or too costly.
- Tolerance averaging — parallel pairs of same-value resistors statistically reduce equivalent tolerance below the individual component tolerance.
- Pull-up and pull-down networks — verifying equivalent resistance and E-series classification for I²C bus termination (typically 1 kΩ to 10 kΩ) and logic-level networks.
- Pre-charge and discharge resistors — checking that capacitor bank discharge resistors remain within power rating during continuous operation.
- Op-amp feedback network verification — confirming that series or parallel feedback resistor combinations yield the correct R_f / R_in ratio and match the intended gain.
Example Calculation
Example 1 — Two 1 kΩ Resistors in Parallel, E24 Match
Inputs: Parallel, R1 = 1 kΩ, R2 = 1 kΩ, tolerance 5% default, E24 target, no V or I applied.
R_eq = (1000 × 1000) / (1000 + 1000) = 500 Ω
Worst-case tolerance:
tol_eq_wc = (R_eq/R1) × 0.05 + (R_eq/R2) × 0.05
= 0.5 × 0.05 + 0.5 × 0.05 = 0.05 = 5.00%
RSS tolerance:
tol_eq_rss = √((0.5×0.05)² + (0.5×0.05)²)
= √(0.000625 + 0.000625) = √0.00125 = 3.54%
E24 matching (500 Ω):
Decade = 2, mantissa = 5.0
Nearest E24: 5.1 (E24 standard value) → 510 Ω
Deviation = (500 − 510) / 510 × 100 = −1.96%
|dev| 1.96% > 0.1% EXACT threshold, ≤ 5% E24 tolerance → NEAR
Result: R_eq = 500 Ω, Nearest E24 = 510 Ω (−1.96%), Tolerance 5.00% WC / 3.54% RSS, Badge: NEAR
The RSS tolerance ±3.54% is 1.46 pp tighter than worst-case ±5% — meaningful for high-volume production.
Example 2 — Three 100 Ω Resistors in Series, OVERLOAD
Inputs: Series, R1 = R2 = R3 = 100 Ω, V = 30 V, power ratings 0.25 W each, E24 target.
R_eq = 100 + 100 + 100 = 300 Ω
I_total = 30 / 300 = 0.1 A = 100 mA
Per resistor:
V_i = 0.1 × 100 = 10 V
P_i = 0.1² × 100 = 1.0 W
util_i = 1.0 / 0.25 = 4.0 = 400%
E24 matching: 300 Ω is an E24 standard value — EXACT (deviation 0%)
Track A: OVERLOAD (util > 100%), Track B EXACT suppressed
Result: R_eq = 300 Ω, Total Power = 3.0 W, Badge: OVERLOAD
Each resistor dissipates 4× its rating. Upsize to 2 W rated parts (next standard rating above P/0.5 = 2.0 W), or reduce applied voltage to √(0.25 × 0.5 / 100) × 300 ≈ 10.6 V.
Example 3 — Series Pair Near 10 kΩ, ADEQUATE / NEAR
Inputs: Series, R1 = 9.1 kΩ, R2 = 1.0 kΩ, V = 10 V, ratings 0.125 W each, tolerance 1% each, E96 target.
R_eq = 9100 + 1000 = 10100 Ω = 10.1 kΩ
I_total = 10 / 10100 = 0.99 mA
P1 = (0.99e-3)² × 9100 = 8.9 mW → util = 8.9/125 = 7.1%
P2 = (0.99e-3)² × 1000 = 0.98 mW → util = 0.98/125 = 0.78%
E96 matching: nearest to 10.1 kΩ is 10.2 kΩ, deviation = −0.98%
|dev| 0.98% ≤ 1% E96 tolerance → NEAR
Track A: ADEQUATE (max util 7.1% < 50%)
Result: R_eq = 10.1 kΩ, Badge: ADEQUATE / NEAR
Standards & References
- IEC 60063 — Preferred number series for resistors and capacitors (E-series definitions E12, E24, E48, E96, E192)
- IEC 60062 — Marking codes for resistors and capacitors (color code and alphanumeric marking)
- IEC 60115 series — Fixed resistors for use in electronic equipment (technical specifications, derating curves)
- MIL-PRF-55342 — Resistors, fixed, film, chip (US military specification with derating practice; via Defense Logistics Agency ASSIST database)
- Ohm's Law (V = I × R) — Fundamental relationship between voltage, current, and resistance
- Kirchhoff's Voltage Law (KVL) — Sum of voltages around a loop equals zero; governs series network voltage division
- Kirchhoff's Current Law (KCL) — Sum of currents into a node equals zero; governs parallel network current division
Units
The calculator uses standard SI electrical units throughout.
- Resistance: ohms (Ω), kilohms (kΩ), megohms (MΩ). Select the unit matching the entered value; the calculator normalizes to Ω internally.
- Voltage: volts (V). Enter applied voltage directly in volts.
- Current: amperes (A). Enter applied current in amperes — for milliampere-range currents, enter as decimal (e.g. 0.05 for 50 mA).
- Power: watts (W). Power ratings and dissipation results are in watts. Standard SMT ratings: 0.063 W, 0.125 W, 0.25 W, 0.5 W, 1 W, 2 W.
- Tolerance: percent (%). Individual tolerance input range: 0% (treated as 'use default') to 50%.
E-series values are unit-agnostic mantissas scaled by powers of 10. The mantissa 4.7 corresponds to 4.7 Ω, 47 Ω, 470 Ω, 4.7 kΩ, 47 kΩ, and so on.
Limitations
- Calculator handles pure series OR pure parallel networks of 2 to 20 resistors. Mixed series-parallel topologies require manual decomposition into sub-networks or external network analysis.
- Resistor values must be positive real numbers. Zero or negative values are not accepted.
- Individual tolerance input range: 0% to 50%. Values of 0 are treated as 'use default tolerance'.
- E48, E96, and E192 nearest values are computed via logarithmic approximation. E12 and E24 use exact enumeration. For E96/E192, the displayed nearest value may differ slightly from the exact IEC 60063 catalog value.
- Power dissipation assumes DC or RMS values. AC circuits with reactive components require separate analysis.
- The 50% derating threshold applies to general-purpose carbon film, metal film, and wirewound resistors. Specialized resistors (high-power, current sense, pulse-rated) may have different derating curves per manufacturer datasheet.
- Voltage priority policy: when both applied voltage and applied current are entered, voltage is used as the source of truth for power calculation.
- Calculator scope excludes voltage divider output ratios, current divider ratios, temperature rise modeling, parasitic effects, noise contribution, and failure mode analysis.
Common Mistakes to Avoid
- Confusing EXACT and NEAR E-series classification. EXACT requires deviation under 0.1%. A deviation of 0.5% is NEAR even for E192 (where the nominal tolerance is 0.5%).
- Assuming worst-case and RSS tolerance are the same. For N identical resistors in series at tol%, worst-case is tol% and RSS is tol% / √N — they diverge significantly for balanced networks.
- Specifying both applied voltage and applied current inconsistently. If V ≠ I × R_eq, the calculator uses applied voltage as the source of truth. Either enter one or verify consistency.
- Assuming two paralleled resistors handle double power without checking math. Two 1 W resistors in parallel handle only 1 W combined at the 50% derating threshold (0.5 W each), not 2 W.
- Using 1/4 W resistors in 30 V series chains without checking dissipation. Three 100 Ω resistors in series with 30 V each dissipate 1 W — four times the rating.
- Treating CUSTOM E-series classification as a design error. CUSTOM means no single standard catalog resistor matches within the chosen series' tolerance band — the combination may be intentional.
- Mixing resistor values in different units without checking normalization. Enter 4.7 kΩ as value=4.7 + unit=kΩ, not value=4700 + unit=kΩ (which would give 4700 kΩ = 4.7 MΩ).
- Entering per-resistor tolerance as a fraction instead of a percentage. Enter 5 for 5%, not 0.05.
Frequently Asked Questions
What is the difference between EXACT, NEAR, and CUSTOM E-series classification?
When should I use worst-case versus RSS tolerance propagation?
Why is per-resistor power shown even when I haven't entered power ratings?
What does the 50% derating threshold mean for resistors?
Can a single standard resistor replace my series or parallel combination?
How does the calculator handle mixed tolerance grades in the same network?
How do I calculate equivalent resistance for resistors in parallel?
Why is RSS tolerance lower than worst-case tolerance?
What happens if I enter both applied voltage and applied current?
Does the E-series I select determine my procurement tolerance?
Can I use this calculator for voltage divider design?
Frequently Used Together
Engineers often use these calculators in combination for complete project workflows:
Related Calculators
Explore similar calculators that might be useful for your project:
Every Electrical Formula. One Free Sheet.
NEC calcs, motor sizing & code coordination — one printable page.
- Instantly check voltage drop, ampacity & motor current
- Catch the 7 wiring errors that fail code inspections
- 12 design checks to run before submitting drawings
No spam. Unsubscribe any time.
Calculate
Series chains resistors end-to-end (same current through all). Parallel connects resistors between the same two nodes (same voltage across all).
Number of resistors in the network (2–20). Shows the corresponding value fields.
Resistor 1 value. Required.
Resistor 2 value. Required.
Applied to each resistor that has no individual tolerance override. Default is 5% commercial grade.
E-series for standard-value matching per IEC 60063. E24 is most common for general-purpose design.
Individual tolerance overrides, power ratings, applied V/I (all optional — leave empty if not needed).