Equivalent Resistance and Ohm’s Law Calculator Online
Ohm’s law and power: enter any two of U, I, R, P and get the rest. Equivalent resistance of a mixed circuit is computed from an expression such as R1 + (R2 ∥ R3), with step-by-step reduction, a circuit diagram and the current, voltage and power of each resistor. Below: a bridge circuit and the star-delta transformation.
Ohm’s law and power
Fill in any two quantities (positive numbers) and we will find the rest.
R = 6 ΩP = 24 W
R = U / I = 12 / 2 = 6 Ω
P = U · I = 12 · 2 = 24 W
Equivalent resistance of a circuit
Series is “+”, parallel is “||” (or “∥”); parallel binds tighter, parentheses are allowed. Numbers are resistances in ohms (4.7k, 1M); names (R1, Rload) get their values below.
Ohm’s law for each resistor: U = I·R, P = U·I. In series the current is common and the voltage splits in proportion to R; in parallel the voltage is common and the current splits in proportion to 1/R. The resistor powers add up to the circuit power — the balance holds.
Bridge circuit
R1 is between A and C, R2 between A and D, R3 between C and B, R4 between D and B, R5 is the bridge diagonal between C and D. The resistance is taken between A and B.
Resistance between A and B: RAB = 23.94 Ω
Replace the triangle R1, R2, R5 with a star whose legs go to A, C and D: Ra = R1·R2 / (R1 + R2 + R5) = 2.5; Rc = R1·R5 / (R1 + R2 + R5) = 6.25; Rd = R2·R5 / (R1 + R2 + R5) = 12.5
Legs Rc + R3 and Rd + R4 are in parallel, then in series with Ra: RAB = Ra + (Rc + R3)(Rd + R4) / (Rc + R3 + Rd + R4) = 23.94 Ω
The bridge is unbalanced: R1·R4 ≠ R2·R3, current flows through R5 and plain series-parallel formulas do not apply.
Star ↔ delta
Delta: R12, R23, R31 between nodes 1, 2, 3. Star: R1, R2, R3 from nodes 1, 2, 3 to a common point.
The current in a circuit section is proportional to the voltage and inversely proportional to the resistance: I = U / R. Power: P = U·I = I²·R = U²/R. Any two of U, I, R, P determine the other two:
U and I: R = U/I, P = U·I;
U and R: I = U/R, P = U²/R;
U and P: I = P/U, R = U²/P;
I and R: U = I·R, P = I²·R;
I and P: U = P/I, R = P/I²;
R and P: U = √(P·R), I = √(P/R).
Series and parallel
In series the same current flows through every resistor and resistances add: R = R₁ + R₂ + …; the voltage splits in proportion to the resistances. In parallel every branch has the same voltage and conductances add: 1/R = 1/R₁ + 1/R₂ + …; for two resistors R = R₁·R₂ / (R₁ + R₂). The current splits inversely to the resistances, and the total is always below the smallest parallel resistor.
Mixed circuits: how to reduce
Find the innermost group whose resistors are purely in series or purely in parallel.
Replace it with one equivalent resistor and redraw the circuit.
Repeat until one resistor is left.
For currents go back: the current of a merged resistor splits among its branches, and a parallel group has one common voltage.
How to enter a circuit
Series is “+”, parallel is “||”, groups go in parentheses. R₁ in series with parallel R₂ and R₃ is written R1 + (R2 || R3). Without parentheses “||” binds tighter than “+”, like multiplication over addition.
Bridge and star-delta
A bridge (five resistors with a diagonal between the midpoints of two branches) cannot be reduced by series-parallel steps alone. Replacing a delta with a star helps: R₁ = R₁₂·R₃₁ / (R₁₂ + R₂₃ + R₃₁) and likewise for the other legs. Back: R₁₂ = R₁ + R₂ + R₁·R₂ / R₃. A bridge is balanced when R₁·R₄ = R₂·R₃: the diagonal current is zero.
Circuits with several sources are solved with Kirchhoff’s laws, AC circuits with the complex method (AC circuits).
FAQ
How do I find the equivalent resistance of a mixed circuit?
Reduce the circuit step by step: replace groups made only of series resistors (sum of R) or only of parallel resistors (1/R = Σ1/Rᵢ) until one resistor remains. The calculator shows every step.
What is the resistance of two equal resistors in parallel?
Half of one of them; for n equal resistors R/n. Two 10 Ω resistors give 5 Ω.
How do I get the power from current and resistance with Ohm’s law?
P = I²·R. The voltage is U = I·R, and the power can also be written as U·I.
What if the circuit contains a bridge?
If R₁·R₄ = R₂·R₃ the diagonal can be removed. Otherwise replace a delta with a star to get an ordinary series-parallel circuit. The “Bridge circuit” block does this automatically.
How do I find the branch currents of a parallel connection?
All branches share the voltage, the branch current is Iᵢ = U/Rᵢ, and the branch currents add up to the total. Set U, I or P of the circuit and the calculator lists the current, voltage and power of every resistor.