How do you calculate resistors in parallel?

For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of each individual resistance: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. The total (equivalent) resistance of a parallel combination is always lower than the smallest individual resistor in the group.

What is the formula for two resistors in parallel?

For exactly two resistors, there is a simplified shortcut: Rtotal = (R1 × R2) ÷ (R1 + R2). This "product over sum" formula is equivalent to the general reciprocal formula but is faster to compute by hand for the common two-resistor case.

Why is the total resistance of a parallel combination always less than the smallest resistor?

Adding a parallel path always gives current an additional route to flow, which increases total conductance (the reciprocal of resistance). Because conductance adds directly in parallel, total conductance is always higher — and total resistance always lower — than any single branch on its own.

Do resistors in parallel share current equally?

Only if they have equal resistance. In general, current divides inversely with resistance — a lower-value resistor in a parallel bank carries proportionally more current than a higher-value one at the same applied voltage, since I = V ÷ R for each branch.

Why would someone put resistors in parallel instead of using one resistor?

Common reasons include: combining standard resistor values to approximate a non-standard value, splitting current across multiple resistors to share power dissipation and reduce heat in any single component, or building redundancy so the circuit still functions (at a different resistance) if one resistor fails open.

Is it safe to parallel two different-value resistors to share power?

Not without care. Because current divides inversely with resistance, mismatched parallel resistors do not share power evenly — the lower-value resistor absorbs more current and more power. If the intent is to share power dissipation, using resistors of equal, matched value (ideally with tight tolerance) in parallel is the more predictable and safer approach, since it keeps power distributed evenly across all branches.

How do I find the current through each resistor in a parallel bank?

If the voltage across the parallel combination is known, the current through each branch is simply that voltage divided by the individual resistor's value: In = V ÷ Rn. This calculator computes this automatically for each resistor when a voltage is entered.

Does adding more resistors in parallel always lower the total resistance?

Yes. Every additional parallel branch, regardless of its value, adds more conductance to the circuit, which can only reduce (or in the theoretical limit, approach but never increase) the total equivalent resistance.

Engineering

Parallel Resistor Calculator

Calculate the equivalent resistance of resistors wired in parallel. Enter up to six values — add a voltage to see current and power split across each branch.

Leave any resistor field blank to exclude it. All values use the unit selected below; convert values into the same unit before entering if your resistors are mixed (e.g., a 1kΩ resistor entered under an "Ω" selection should be typed as 1000).

Resistor values

Unit for all values above

Applied voltage (V) — optional

Equivalent resistance

—

Resistors used—

Total current (if voltage given)—

Total power (if voltage given)—

How parallel resistance is calculated

When resistors are connected in parallel, they each provide an independent path for current between the same two nodes. Instead of resistances adding directly, their conductances (the reciprocal of resistance) add together, which is why the combined resistance formula uses reciprocals and always yields a value lower than the smallest branch.

If a voltage is supplied, this calculator also finds the current through each individual resistor (V ÷ Rn) and its power dissipation (V² ÷ Rn), which is useful for checking whether any single resistor in the bank is carrying a disproportionate share of the current.

Formula steps

General (any number of resistors): 1 ÷ Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn Rtotal = 1 ÷ (1/R1 + 1/R2 + ... + 1/Rn) Shortcut for exactly two resistors: Rtotal = (R1 × R2) ÷ (R1 + R2) If voltage V is known, for each resistor Rn: In = V ÷ Rn Pn = V² ÷ Rn Total current = sum of all In Total power = sum of all Pn (also equals V² ÷ Rtotal)

Safety guidance: current hogging in parallel banks

Because current splits inversely with resistance, mismatched resistors in parallel do not share load evenly. If the goal is to combine resistors to jointly handle more power than one part could alone, the lowest-value resistor in an uneven bank will absorb a larger share of both current and power — it can overheat and fail even while other resistors in the same bank run comfortably within their rating.

For power-sharing applications, using resistors of the same value and the same rated power (ideally the same batch or tight tolerance) gives a much more predictable, even split. When mixing different values by necessity — for example, to reach a non-standard resistance — check the individual current and power figures this calculator reports for each branch, and rate every resistor in the bank for its own calculated dissipation, not an average of the total.

Code cautions

This calculator addresses component-level resistor math and is not a substitute for the requirements of the National Electrical Code or an equivalent code where parallel conductor sizing, overcurrent protection, or paralleled power resistors are used in a real installation (for example, paralleled shunt resistors, ballast resistors, or load banks). Any parallel resistor arrangement carrying meaningful power in a permanent installation should be reviewed for thermal management, spacing, and — where applicable — code-required conductor and enclosure requirements by a qualified engineer or electrician.

Design limitations of this calculator

Ideal resistors assumed: component tolerance (commonly ±1% to ±10%), temperature coefficient, and aging drift are not modeled — real parallel combinations will vary slightly from the calculated ideal value.
No wiring or contact resistance: connections between paralleled resistors are assumed to have zero resistance, which is not true in practice, especially with long or thin interconnects.
DC / low-frequency behavior only: parasitic inductance and capacitance, which become significant at high frequencies, are not modeled.
No thermal interaction modeling: resistors mounted close together can heat each other, changing their effective resistance and power handling in ways this calculator does not account for.
Six-resistor limit: for combinations larger than six branches, apply the general reciprocal formula iteratively or in a spreadsheet.

Frequently asked questions

For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of each individual resistance: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn. The total (equivalent) resistance of a parallel combination is always lower than the smallest individual resistor in the group.
For exactly two resistors, there is a simplified shortcut: Rtotal = (R1 × R2) ÷ (R1 + R2). This "product over sum" formula is equivalent to the general reciprocal formula but is faster to compute by hand for the common two-resistor case.
Adding a parallel path always gives current an additional route to flow, which increases total conductance (the reciprocal of resistance). Because conductance adds directly in parallel, total conductance is always higher — and total resistance always lower — than any single branch on its own.
Only if they have equal resistance. In general, current divides inversely with resistance — a lower-value resistor in a parallel bank carries proportionally more current than a higher-value one at the same applied voltage, since I = V ÷ R for each branch.
Common reasons include: combining standard resistor values to approximate a non-standard value, splitting current across multiple resistors to share power dissipation and reduce heat in any single component, or building redundancy so the circuit still functions (at a different resistance) if one resistor fails open.
Not without care. Because current divides inversely with resistance, mismatched parallel resistors do not share power evenly — the lower-value resistor absorbs more current and more power. If the intent is to share power dissipation, using resistors of equal, matched value (ideally with tight tolerance) in parallel is the more predictable and safer approach, since it keeps power distributed evenly across all branches.
If the voltage across the parallel combination is known, the current through each branch is simply that voltage divided by the individual resistor's value: In = V ÷ Rn. This calculator computes this automatically for each resistor when a voltage is entered.
Yes. Every additional parallel branch, regardless of its value, adds more conductance to the circuit, which can only reduce (or in the theoretical limit, approach but never increase) the total equivalent resistance.