Circuit Analysis calculator

Parallel Resistor Calculator

Calculate equivalent resistance, current distribution, and branch power for parallel resistors. For example, 100Ω, 200Ω, and 300Ω at 12 V give 54.55Ω equivalent resistance, 220 mA total current, and 1.44 W in the 100Ω branch.

Updated June 2, 2026

1/Req = 1/R1 + 1/R2 + 1/R3...

Two 100Ω parallel = 50Ω | Three 100Ω = 33.3Ω

Enter resistor values for equivalent resistance

Calculator Inputs

Quick Presets

Calculation Results

Enter values above to see calculation results

Calculation history

Example Calculations

LED Current Limiting - Parallel 220Ω Resistors

Two 220Ω 1/4W resistors in parallel for 5V LED array (30mA total)

Inputs

Calculation Mode: Two resistors
Resistor 1: 220
Resistor 2: 220
Voltage: 5

Current Divider - 100Ω and 200Ω at 12V

2:1 current division for dual-supply circuit

Inputs

Calculation Mode: Two resistors
Resistor 1: 100
Resistor 2: 200
Voltage: 12

How to Use

Parallel Resistor Formula Quick Reference

Configuration	Formula	Example
2 Resistors	R_eq = (R₁ × R₂)/(R₁ + R₂)	(100 × 200)/(100+200) = 66.7Ω
2 Equal Resistors	R_eq = R/2	1kΩ \|\| 1kΩ = 500Ω
n Resistors	1/R_eq = 1/R₁ + 1/R₂ + ... + 1/R_n	1/R_eq = 1/100 + 1/220 + 1/330
Current Division (2R)	I₁ = I_total × R₂/(R₁+R₂)	I₁ = 100mA × 200/(100+200) = 66.7mA
Current Division (n R)	I_n = V/R_n (same V across all)	I = 5V/100Ω = 50mA
Power per Resistor	P_n = V²/R_n	P = 5²/100 = 250mW

Parallel vs. Series Resistor Comparison

Parameter	Parallel Configuration	Series Configuration
Equivalent R	1/Req = 1/R₁ + 1/R₂ (R_eq < R_min)	Req = R₁ + R₂ (R_eq > R_max)
Voltage	Same across all (V₁ = V₂ = V_total)	Divides (V_total = V₁ + V₂)
Current	Divides (I_total = I₁ + I₂)	Same through all (I₁ = I₂ = I_total)
Example (100Ω, 200Ω)	Req = 66.7Ω (lower than 100Ω)	Req = 300Ω (higher than 200Ω)
Primary Use	Current division, lower resistance	Voltage division, higher resistance

Key Principles (Kirchhoff's Current Law)

R_eq < R_min: Parallel resistance is always less than the smallest individual resistor
Same Voltage: All parallel resistors have identical voltage across them (V₁ = V₂ = V₃...)
Current Sum: Total current equals sum of branch currents (I_total = I₁ + I₂ + I₃...)
Inverse Current Division: Lower resistance → Higher current (I ∝ 1/R)
Power Distribution: Lower resistance → Higher power dissipation (P ∝ 1/R)

Standard E12/E24 Resistor Series for Parallel 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 Parallel Combinations: 100Ω || 100Ω = 50Ω, 220Ω || 330Ω = 132Ω, 1kΩ || 2.2kΩ = 688Ω. For non-standard values, parallel standard resistors to achieve target resistance. Always verify power ratings: lower value resistors carry more current and dissipate more power.

Practical Engineering Considerations

Consideration	Impact	Best Practice
Tolerance Effects	±10% on 100Ω\|\|100Ω → 90\|\|90=45Ω to 110\|\|110=55Ω range	Use ±1% (E96) or ±5% (E24) for precision. Calculate worst-case: parallel of min values and max values.
Power Derating	Lower R dissipates more power (P ∝ 1/R)	Per manufacturer derating curve: Derate to 70% at 70°C, 50% at 125°C. 1/4W (250mW) → 175mW at 70°C, 125mW at 125°C.
Temperature Coefficient	±100ppm/°C causes ±1% drift over 100°C	Match TC specs for parallel resistors. Use metal film (±50ppm/°C) for stability.
PCB Layout	Unequal trace resistance causes current imbalance	Use equal-length, equal-width traces for precision current division.
Thermal Coupling	Heat transfer between resistors changes R values	Space ≥5mm apart for >0.5W dissipation. Use thermal modeling for high-power.

Design Tips: (1) For LED current limiting, parallel resistors halve power per component but require matched values for equal current sharing. (2) Current divider precision improves with lower resistance values (less sensitive to tolerance). (3) When creating custom values, choose combinations where smallest R carries <80% of total current to avoid thermal runaway. (4) For high-frequency AC, consider parasitic inductance in wire-wound resistors - use metal film or thick film for >1MHz.

Calculation Instructions

Enter resistance values in ohms (Ω), kilohms (kΩ), or megohms (MΩ). Optionally specify applied voltage to calculate individual currents, power dissipation, and verify component ratings. Calculator determines: (1) Equivalent parallel resistance, (2) Individual branch currents (if voltage provided), (3) Power dissipation per resistor, (4) Conductance contribution percentages. For current divider design, use inverse ratio: R₁/R₂ = I₂/I₁.

Common Applications

LED Arrays - Parallel resistors reduce power dissipation per component while achieving target current (e.g., 2×220Ω for 110Ω equivalent)

Current Dividers - Design precise current ratios for sensor biasing (R1/R2 = I2/I1 inverse relationship)

Power Distribution - Equal-value parallel resistors share load current equally, reducing thermal stress

Custom Resistor Values - Achieve non-standard values from E12/E24 series (e.g., 100Ω||220Ω||470Ω = 62Ω)

Pull-up/Pull-down Networks - Lower equivalent resistance for faster signal transitions in digital circuits

Shunt Resistors - Parallel high-power resistors for current sensing in power electronics

Impedance Matching - Fine-tune input/output impedance in RF and audio circuits

Thermal Management - Distribute power dissipation across multiple components to reduce hotspots

Frequently Asked Questions

How do I calculate equivalent resistance for parallel resistors and why is it always lower?

For parallel resistors, use the formula: 1/Rtotal = 1/R1 + 1/R2 + 1/R3... For two resistors: Rtotal = (R1 × R2)/(R1 + R2). For example, 100Ω and 200Ω in parallel: Rtotal = (100 × 200)/(100 + 200) = 66.7Ω. The equivalent resistance is always less than the smallest individual resistor because parallel resistors provide multiple current paths, reducing total circuit resistance. Adding more parallel paths always decreases equivalent resistance since adding positive terms to 1/Rtotal increases the sum, which decreases Rtotal.

How does current divide in parallel resistor circuits and how do I design current dividers?

Current divides inversely proportional to resistance values - higher current flows through lower resistance paths. For two resistors: I1 = Itotal × (R2/(R1 + R2)) and I2 = Itotal × (R1/(R1 + R2)). Total current equals the sum of individual currents per Kirchhoff's Current Law. To design current dividers, choose resistor values for desired current ratios: for equal current division, use equal resistances; for specific ratios, use R1/R2 = I2/I1 (inverse relationship). Consider power ratings, tolerance effects, and temperature coefficients for precision applications.

How do I calculate power dissipation in parallel resistor circuits?

Each resistor dissipates power based on P = V²/R, where V is the same across all parallel resistors. Lower resistance resistors dissipate more power since power is inversely proportional to resistance. Total power equals the sum of individual power dissipations: Ptotal = P1 + P2 + P3... Always verify that individual resistor power ratings are not exceeded, especially for the lowest resistance values which carry the highest current and dissipate the most power.

What are common design errors when using parallel resistors and how do I avoid them?

Common errors: (1) Forgetting power derating - operate at 50-70% of rated power per manufacturer derating curve, not 100%. (2) Ignoring tolerance stack-up - ±10% resistors can cause ±22% variation in parallel combinations. (3) Assuming equal current sharing with unequal values - current divides inversely with resistance (I₁/I₂ = R₂/R₁). (4) Thermal coupling - place high-power resistors ≥5mm apart to prevent thermal runaway. (5) PCB trace resistance - use equal-length traces for precision current division; 1Ω trace resistance on 10Ω resistor causes 10% error. (6) High-frequency parasitic effects - wire-wound resistors have inductance; use metal film for >1MHz applications.