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. |
Frequently Asked Questions - Thevenin Voltage Calculator:
What is Thevenin voltage (Vth)?
Vth is the open-circuit voltage at two terminals of a linear circuit (voltage seen with the load removed).
How to calculate Vth?
Remove the load and compute the open-circuit voltage across the terminals using voltage division, superposition, or source transforms.
How to find Rth?
Deactivate independent sources (short voltage, open current) and compute equivalent resistance seen into the terminals.
How to get Norton equivalent?
Convert Thevenin: I_N = Vth / Rth; Norton is I_N in parallel with Rth.
When is Thevenin useful?
To simplify load analysis, compute load voltage/power quickly, and for circuit design and matching.
Can I use superposition for Vth?
Yes — superposition or the weighted-resistor formula works for multiple sources connected via resistances to the node.
How does source transform help?
A current source || R can be converted to a voltage source series R (V=I·R) to simplify Vth calculation.
Do dependent sources change Rth method?
Yes — with dependent sources, Rth must be found by applying a test source at the terminals and calculating the resulting voltage/current.
What units for Rth and Vth?
Vth in volts (V), Rth in ohms (Ω); Norton current in amperes (A).
What if circuit is non-linear?
Thevenin applies only to linear circuits (linear resistors and independent/dependent sources). Nonlinear elements invalidate the simple Thevenin equivalent.
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