Thevenin Equivalent Calculator

Thevenin Equivalent Calculator – Electrical Circuit Analysis Tool :root { –primary-color: #0056b3; –secondary-color: #f8f9fa; –border-color: #dee2e6; –text-color: #333; –accent-color: #e67e22; } body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; line-height: 1.6; color: var(–text-color); max-width: 800px; margin: 0 auto; padding: 20px; } .calculator-wrapper { background: #fff; border: 1px solid var(–border-color); border-radius: 8px; padding: 30px; box-shadow: 0 4px 6px rgba(0,0,0,0.05); margin-bottom: 40px; } .calculator-header { text-align: center; margin-bottom: 25px; } .circuit-diagram { text-align: center; margin: 20px 0; padding: 15px; background: var(–secondary-color); border-radius: 4px; border: 1px dashed #aaa; } .circuit-desc { font-size: 0.9em; color: #666; font-style: italic; margin-top: 5px; } .input-group { margin-bottom: 20px; } .input-group label { display: block; margin-bottom: 8px; font-weight: 600; } .input-wrapper { display: flex; align-items: center; } .input-wrapper input { flex: 1; padding: 12px; border: 1px solid var(–border-color); border-radius: 4px 0 0 4px; font-size: 16px; } .input-unit { background: var(–secondary-color); padding: 12px 15px; border: 1px solid var(–border-color); border-left: none; border-radius: 0 4px 4px 0; color: #666; font-weight: 500; min-width: 40px; text-align: center; } button.calc-btn { width: 100%; padding: 15px; background-color: var(–primary-color); color: white; border: none; border-radius: 4px; font-size: 18px; font-weight: bold; cursor: pointer; transition: background-color 0.2s; } button.calc-btn:hover { background-color: #004494; } #results-container { margin-top: 30px; padding-top: 20px; border-top: 2px solid var(–border-color); display: none; } .result-row { display: flex; justify-content: space-between; align-items: center; padding: 15px 0; border-bottom: 1px solid #eee; } .result-label { font-weight: 600; color: #555; } .result-value { font-size: 1.25em; font-weight: 700; color: var(–primary-color); } .norton-section { margin-top: 15px; background: #fff3cd; padding: 15px; border-radius: 4px; color: #856404; } .content-section { margin-top: 50px; } h2 { color: var(–primary-color); margin-top: 30px; } h3 { color: #333; margin-top: 25px; } .formula-box { background: var(–secondary-color); padding: 15px; border-left: 4px solid var(–accent-color); font-family: "Courier New", monospace; margin: 15px 0; overflow-x: auto; } ul { margin-bottom: 20px; } li { margin-bottom: 10px; } .error-msg { color: #dc3545; text-align: center; margin-top: 10px; display: none; }

Thevenin Equivalent Calculator

Compute Vth and Rth for standard voltage divider circuits

+ – Vs R1 R2 A B
Topology: Voltage Source (Vs) in series with R1, connected to load resistor R2 (parallel).
Output is across terminals A and B (across R2).
V
Ω
Ω
Please enter valid numeric values for all fields. Resistors must be non-negative.

Thevenin Equivalent Results

Thevenin Voltage (Vth): –
Thevenin Resistance (Rth): –
Norton Current (IN): –
(Short Circuit Current Isc)

What is Thevenin's Theorem?

Thevenin's Theorem is a fundamental principle in electrical engineering theory. It states that any linear electrical network containing only voltage sources, current sources, and resistances can be replaced at terminals A-B by an equivalent combination of a single voltage source (Vth) in a series connection with a single resistance (Rth).

This simplification is incredibly powerful for circuit analysis, allowing engineers to focus on how a load (connected between terminals A and B) interacts with the rest of the circuit without recalculating the entire network every time the load changes.

Formulas Used in This Calculator

This calculator assumes a standard voltage divider circuit topology where a voltage source ($V_s$) is in series with a resistor ($R_1$), and we are looking at the output across a parallel resistor ($R_2$).

Thevenin Voltage (Vth):
Vth = Vs × [ R2 / (R1 + R2) ]
Thevenin Resistance (Rth):
Rth = (R1 × R2) / (R1 + R2)
Norton Current (IN):
IN = Vth / Rth

How to Calculate Manually

To find the Thevenin equivalent of a circuit manually, follow these two main steps:

  1. Find Vth (Open Circuit Voltage): Remove the load resistor (if any) and calculate the voltage across the open terminals A and B. In our voltage divider configuration, this is simply the voltage drop across R2.
  2. Find Rth (Equivalent Resistance): Turn off all independent sources. Replace voltage sources with a short circuit (wire) and current sources with an open circuit. Then, calculate the total resistance looking back into terminals A and B. For the circuit above, shorting Vs places R1 and R2 in parallel.

Why is this important?

  • Simplification: Reduces complex networks to a simple 2-component model.
  • Load Analysis: Makes it easy to calculate voltage regulation and power transfer for varying loads.
  • Maximum Power Transfer: The theorem is essential for determining the load resistance required to achieve maximum power transfer (which occurs when RLoad = Rth).

Example Calculation

Suppose you have the following circuit parameters:

  • Source Voltage (Vs) = 24V
  • Series Resistor (R1) = 100Ω
  • Parallel Resistor (R2) = 300Ω

Step 1: Calculate Vth

Vth = 24 × (300 / (100 + 300)) = 24 × 0.75 = 18 V

Step 2: Calculate Rth

Rth = (100 × 300) / (100 + 300) = 30000 / 400 = 75 Ω

function calculateThevenin() { // Get input elements var vsInput = document.getElementById("voltageSource"); var r1Input = document.getElementById("resistor1"); var r2Input = document.getElementById("resistor2"); var errorMsg = document.getElementById("errorMessage"); var resultContainer = document.getElementById("results-container"); // Parse values var vs = parseFloat(vsInput.value); var r1 = parseFloat(r1Input.value); var r2 = parseFloat(r2Input.value); // Validation // R values typically shouldn't be negative. 0 is edge case (short). // Vs can be negative. if (isNaN(vs) || isNaN(r1) || isNaN(r2)) { errorMsg.style.display = "block"; resultContainer.style.display = "none"; return; } if (r1 < 0 || r2 < 0) { errorMsg.innerText = "Resistors cannot have negative resistance."; errorMsg.style.display = "block"; resultContainer.style.display = "none"; return; } // Check for division by zero in R calculation if ((r1 + r2) === 0) { errorMsg.innerText = "Total series resistance cannot be zero (Short Circuit)."; errorMsg.style.display = "block"; resultContainer.style.display = "none"; return; } // Hide error if valid errorMsg.style.display = "none"; // Calculations // Vth formula: Voltage Divider var vth = vs * (r2 / (r1 + r2)); // Rth formula: Parallel resistors (since Vs is shorted) var rth = (r1 * r2) / (r1 + r2); // Norton Current (I_N or I_sc) = Vth / Rth // If Rth is 0, Current is infinite (theoretically) var iNorton = 0; if (rth !== 0) { iNorton = vth / rth; } else { iNorton = Infinity; } // Formatting results // Helper function to format metric prefixes if desired, // but for simplicity we will stick to fixed decimals or scientific notation for very large/small nums. function formatValue(num, unit) { if (Math.abs(num) 10000) { return num.toExponential(3) + " " + unit; } else { return num.toFixed(3) + " " + unit; } } document.getElementById("resVth").innerText = formatValue(vth, "V"); document.getElementById("resRth").innerText = formatValue(rth, "Ω"); document.getElementById("resIn").innerText = formatValue(iNorton, "A"); // Show results resultContainer.style.display = "block"; }

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