LED Series Resistor Calculator mechanism

Model scope

The core ideal formulas are standard under the stated assumptions, but the specification is not complete enough for an unambiguous production calculator. Define the resistor series, tolerance, rounding direction, selected-value power recalculation, recommended derating margin, and input validation rules. The empty honest_label should be replaced with a disclosure that this is an ideal estimate and does not account for LED, supply, thermal, or tolerance variation.

• R=(Vs−nVf)/If is correct for identical LEDs connected in series, with If expressed in amperes, provided Vs exceeds nVf.
• P=I²R is correct for resistor dissipation when I=If and R is the resistor's actual installed resistance. If a standard resistor value is selected, power should also be recalculated using that selected value.
• The meaning of 'nearest standard value' is unspecified: no E-series, tolerance, or rounding direction is defined. For current limiting, rounding up is generally safer than mathematically nearest rounding.
• 'Resistor power rating' has no defined formula. Calculated dissipation is not a sufficient rating; a safety margin, tolerance, temperature derating, and continuous-versus-pulse operation must be specified.
• The series LED count must be a positive integer, and the formula assumes the LEDs have the same forward voltage and share the same current.

Units and conventions

• Vs and Vf are in volts.
• If is converted to amperes before calculation; for example, 20 mA = 0.020 A.
• n is a dimensionless positive integer.
• R is in ohms and P is in watts.
• The test vectors use mathematical nearest rounding to the E12 resistor series only; the specification does not currently define this convention.
• The shown power value is ideal continuous dissipation at the exact calculated resistance, not a final recommended commercial power rating.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "supply_V": 5,
    "LED_forward_voltage_V": 2,
    "series_count": 2,
    "target_current_A": 0.02
  },
  "expected_outputs": {
    "R_exact_ohm": 50,
    "P_exact_R_W": 0.02,
    "nearest_standard_value_E12_ohm": 47,
    "minimum_continuous_rating_before_margin_W": 0.02
  },
  "working": "Voltage across resistor = 5 − (2 × 2) = 5 − 4 = 1 V. R = 1 / 0.020 = 50 ohm. P = I²R = 0.020² × 50 = 0.0004 × 50 = 0.020 W. Nearest E12 values are 47 ohm and 56 ohm; |50−47|=3 and |56−50|=6, so nearest = 47 ohm."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The calculator can encounter undefined output at If=0, can produce zero or negative resistance at and below the LED forward-voltage boundary, and can produce results differing by a factor of 1000 or more when current units are ambiguous. These cases require rejection, warning, or explicit unit handling.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json