If you are building a linear power supply, the direct answer for your LM317T calculator needs is this: the standard output voltage formula is Vout = Vref × (1 + R2 / R1) + (Iadj × R2). For a standard 5.0V output using a 240Ω R1 resistor, you need an R2 value of approximately 713Ω. While many basic online calculators ignore the adjustment pin current (Iadj), ignoring it introduces voltage drift that will fail precision analog circuits. Below, we derive the exact math, track the units through real bench scenarios, and provide a concrete decision tree to pick your exact bill of materials.
The Core LM317T Output Voltage Formula
The LM317T is a floating, three-terminal adjustable linear regulator. It maintains a constant 1.25V reference voltage (Vref) between its output and adjust pins. The resistor divider network (R1 and R2) scales this reference up to your target output voltage. However, a small bias current (Iadj) flows out of the adjust pin and through R2, adding a slight voltage offset.
The complete, datasheet-accurate formula is:
Vout = Vref × (1 + R2 / R1) + (Iadj × R2)
| Symbol | Parameter | Typical Value / Magnitude | Unit |
|---|---|---|---|
| Vout | Target Output Voltage | 1.25V to 37V | Volts (V) |
| Vref | Internal Reference Voltage | 1.25V (Range: 1.20V - 1.30V) | Volts (V) |
| R1 | Program Resistor (Output to Adj) | 120Ω to 240Ω | Ohms (Ω) |
| R2 | Set Resistor (Adj to Ground) | 0Ω to 5,000Ω | Ohms (Ω) |
| Iadj | Adjustment Pin Bias Current | 50μA (Max 100μA) | Amperes (A) |
Rearranged Forms: Solving for R1, R2, and Vout
When using an LM317T calculator, you rarely solve for Vout from scratch; you usually have a target voltage and need to find the resistor values. Here are the algebraically rearranged forms with Iadj preserved for precision.
1. Solving for R2 (Given Vout and R1):
R2 = (Vout - Vref) / [ (Vref / R1) + Iadj ]
This is the most common calculation. You pick a standard R1 (like 240Ω) and calculate the exact R2 needed to hit your target voltage.
2. Solving for R1 (Given Vout and R2):
R1 = (Vref × R2) / [ Vout - Vref - (Iadj × R2) ]
Use this when you are scavenging parts from a bin and have a fixed R2 value or a specific potentiometer you want to use, and need to find the matching R1 to set the baseline.
Worked Examples with Unit Tracking
Abstract formulas cause wiring mistakes. Let us track the units through two distinct bench scenarios to prove the math and highlight where Iadj matters.
Problem 1: Designing a 5.0V USB Power Supply
Goal: Vout = 5.0V. We choose R1 = 240Ω to guarantee a ~5.2mA minimum load (1.25V / 240Ω). Assume Vref = 1.25V and Iadj = 50μA (0.00005A). Find R2.
Step 1: Convert all units to base SI (Volts, Ohms, Amperes).
- Vout = 5 V
- Vref = 1.25 V
- R1 = 240 Ω
- Iadj = 0.00005 A
Step 2: Plug into the rearranged R2 formula.
R2 = (5 - 1.25) / [ (1.25 / 240) + 0.00005 ]
Step 3: Solve the denominator (current terms).
- Current through R1 = 1.25 V / 240 Ω = 0.005208 A
- Total denominator = 0.005208 A + 0.00005 A = 0.005258 A
Step 4: Solve the numerator (voltage drop across R2).
- Numerator = 5 V - 1.25 V = 3.75 V
Step 5: Final Division.
R2 = 3.75 V / 0.005258 A = 713.19 Ω
Result: You need a 713Ω resistor. If you used the simplified formula (ignoring Iadj), you would calculate 720Ω. The 7Ω difference is negligible for a 5% tolerance carbon film resistor, but if you are trimming a precision 1% circuit, that 7Ω error shifts your output by roughly 36mV.
Problem 2: High-Voltage 24V Supply for Relay Coils
Goal: Vout = 24.0V. Because the output voltage is high, R2 will be large, making the Iadj voltage drop significant. We drop R1 to 120Ω to increase the divider current and minimize the Iadj error percentage. Find R2.
Step 1: Base SI Units.
- Vout = 24 V, Vref = 1.25 V, R1 = 120 Ω, Iadj = 0.00005 A
Step 2: Denominator (Current).
- R1 current = 1.25 V / 120 Ω = 0.010416 A
- Total denominator = 0.010416 A + 0.00005 A = 0.010466 A
Step 3: Numerator (Voltage).
- 24 V - 1.25 V = 22.75 V
Step 4: Final Division.
R2 = 22.75 V / 0.010466 A = 2173.7 Ω
Result: You need a 2.17kΩ resistor. If we had ignored Iadj here, the math would yield 2184Ω. The 10Ω discrepancy is small, but notice how dropping R1 to 120Ω forced the divider current to 10.4mA, effectively drowning out the 50μA Iadj error. This is why ON Semiconductor application notes recommend lower R1 values for high-voltage outputs.
Assumptions, Boundaries, and Unit Traps
The LM317T calculator formula assumes ideal conditions. If you violate the physical boundaries of the silicon, the math will not match the multimeter reading on your bench.
When the Formula Applies (and When It Fails)
- Dropout Voltage: The formula assumes Vin is at least 3V higher than Vout. If you want 12V out, you must feed it at least 15V in. If Vin drops to 13V, the LM317T drops out of regulation, and Vout will simply be Vin minus ~1.5V, regardless of your resistor math.
- Minimum Load Current: The formula assumes the regulator is sourcing at least 10mA. If your load is a high-impedance op-amp drawing 2mA, the output voltage will float high. You must add a dummy load resistor from Vout to GND to guarantee the 10mA minimum.
- Thermal Shutdown: The formula ignores power dissipation. Pdissipated = (Vin - Vout) × Iload. A bare TO-220 package can only dissipate ~1.5W before hitting thermal shutdown. If you step 24V down to 5V at 1A, you are dissipating 19W. The chip will thermally throttle, and your output will collapse to zero.
The Unit Mistakes That Break the Math
The most common way hobbyists break this formula is through unit mismatch in the Iadj term.
Decision Path: Picking Your R1 and R2 Values
Stop guessing resistor values. Use this decision tree to lock in your exact component picks based on your specific project requirements.
| Condition / Constraint | Action / Rule | Reasoning |
|---|---|---|
| Target Vout is between 1.25V and 15V | Set R1 = 240Ω | Draws 5.2mA, satisfying minimum load without wasting excessive power as heat. |
| Target Vout is between 15V and 37V | Set R1 = 120Ω | Increases divider current to 10.4mA, minimizing the percentage error introduced by Iadj across large R2 values. |
| Load draws less than 10mA continuously | Add 120Ω dummy load from Vout to GND | Guarantees the internal bandgap reference stays in regulation under no-load conditions. |
| Vin - Vout > 5V AND Iload > 0.2A | Calculate Pdiss. If > 1.25W, add heatsink. | Prevents the internal thermal shutdown circuit from collapsing your output voltage. |
| Need adjustable output (Bench Supply) | Use fixed R2 + Potentiometer in series | Prevents the wiper noise of a standalone pot from causing wild voltage oscillations. |
The Concrete BOM Pick
For 90% of hobbyist variable bench power supplies targeting the 1.25V to 12V range, do not overcomplicate the design. Execute the following concrete pick:
- R1: Buy a 240Ω 1/4W 1% Metal Film Resistor (Standard E96 series value). Do not use 5% carbon film; the tolerance will shift your baseline Vref scaling.
- R2 Base: Buy a 390Ω 1/4W 1% Metal Film Resistor. This sets your absolute floor above the 1.25V minimum.
- R2 Adjust: Buy a 2kΩ Linear (B-Taper) Trimmer Potentiometer (e.g., Bourns 3296W series). Wire it in series with the 390Ω base resistor.
This exact combination guarantees your output will smoothly adjust from roughly 3.3V up to 14.5V, keeps the Iadj error below 15mV, and ensures the regulator never drops out of regulation at no-load. Solder a 1μF tantalum capacitor directly across the output pins to improve transient response, and your LM317T power supply is complete.
