Thevenin Voltage Calculator
Easily calculate Thevenin voltage and resistance. Find Vth, Rth, and Norton equivalents using formulas, examples, and step-by-step methods.
Norton equivalent calculator
Thevenin voltage of a circuit is computed by opening the load terminals before finding the open-circuit voltage across the load terminals (Vth) by either open-circuit voltage division or open-circuit voltage superposition. Then compute the input resistance of the terminals by deactivation of independent sources and calculus of the input resistance. Vth in series with Rth is the Thevenin equivalent - it is helpful in the rapid prediction of load voltage and power.
Formula & Table Summary:
- Open-circuit (Thevenin) voltage: Vth = VOC (voltage across terminals with load removed).
- Thevenin resistance: Rth = Req (looking into terminals with independent sources deactivated: voltage sources → short, current sources → open).
- Norton conversion: IN = Vth / Rth; Norton: IN in parallel with Rth.
- Superposition for Vth (two-source weighted average): For two sources through resistances R1,R2 to the node: \( V_{th}=\dfrac{V_1/R_1 + V_2/R_2 + \dots}{1/R_1 + 1/R_2 + \dots}\)
- Source transform (current ↔ voltage): V = I·R (current source I in parallel R ↔ voltage source V=I·R in series R).
Converter Table (Input → Output)
| Input (circuit type) | Method / Formula | Output |
|---|---|---|
| Single source + resistors (voltage divider) | Vth = Vsource × (Ropen / (Rseries + Ropen)) | Vth (V) |
| Multiple sources via resistors | Superposition or weighted average: Vth = (Σ Vi/Ri) / (Σ 1/Ri) | Vth (V) |
| Current source || R | Source transform: V = I·R → then use voltage-divider | Vth, Rth |
| Find Rth | Deactivate independent sources; find equivalent R seen into terminals | Rth (Ω) |
| Want Norton form | I_N = Vth / Rth | I_N (A) and Rth (Ω) |
Thevenin voltage calculator
The Thevenin voltage ( V th ) is the voltage at the open terminals of a linear circuit - the voltage that a load would observe in case the load was not connected. To determine V th, wave off the load, calculate the voltage on the open terminals (voltage division, superposition, source transformations). Rth Thevenin resistance is determined by neutralizing the independent sources (otherwise called short voltage sources, open current sources) and measuring the equivalent resistance into the terminals. Its Thevenin equivalent is then just one voltage source V th in series with R th or Norton current source In = V th/R th in parallel with R th. This eases load analysis, quick power checking, and is needed in designing circuit simplification, instrumentation, and control.
electrical engineering tool
| Scenario | Input | Calculation | Result |
|---|---|---|---|
| A — Voltage divider | Vsrc=12 V series R1=1 kΩ to node A, node A to ground via R2=2 kΩ. Vth measured at node A (open). | Vth = 12 × (R2/(R1+R2)) = 12 × (2000/(1000+2000)) | Vth = 12 × 2/3 = 8.00 V. Rth = R1 || (R2 open → R1) so Rth = R1 = 1 kΩ (looking into node A with source shorted) |
| B — Two sources into node (superposition / weighted average) | V1=12 V via R1=1 kΩ, V2=6 V via R2=2 kΩ, both connected to node A (no load). | Vth = (V1/R1 + V2/R2) / (1/R1 + 1/R2) = (12/1000 + 6/2000) / (0.001 + 0.0005) | Numerator=0.012+0.003=0.015; Denom=0.0015; Vth=0.015/0.0015=10.00 V. Rth = R1 || R2 = (1000×2000)/(3000)=666.67 Ω |
| C — Current source → Thevenin (source transform) | Current source I = 5 mA in parallel with R = 2 kΩ; terminals across the parallel pair (open). | Transform to V = I·R = 0.005×2000 = 10 V series 2 kΩ ⇒ Vth = 10 V, Rth = 2 kΩ | Vth = 10.00 V; Rth = 2.00 kΩ; Norton In = Vth/Rth = 10/2000 = 5 mA (consistent) |
| D — Rth find with independent sources | Two resistors R1=1 kΩ and R2=2 kΩ in series with a voltage source to terminal pair; deactivate source (short). | With source shorted R1 and R2 become parallel when measuring across terminals depending on connection. Example: if terminals across R2, Rth seen = R1 || R2, etc. (apply circuit-specific reduction). | Example result depends on topology; use short/open sources then reduce resistors to find numeric Rth. |
