DC Lighting Voltage Drop Formulas

DC lighting voltage drop formulas: the loop drop of a two-wire run, the drop as a share of the supply, the longest run for a limit and a distributed strip load.

The formulas

P is the load power, V the supply voltage, ρ the resistivity of the conductor (1.72 × 10⁻⁸ Ω·m for copper at about 20 °C), A the cross-section and L the one-way length. The factor 2 counts the supply and the return conductor. A hot cable has a higher resistance than the cold value. A constant-current LED driver keeps its output current while the voltage falls, but a fixture on a plain constant-voltage supply gets less voltage and may dim or fail to start. The limit of 3% and the loads here are examples, and the standard or the fixture maker sets the real limit.

Worked example: a 50 W fixture on a 24 V supply, 10 m of 1.5 mm² copper

1. I = 50 / 24 = 2.083 A
2. r = 1.72 × 10⁻⁸ / (1.5 × 10⁻⁶) = 0.01147 Ω/m
3. ΔV = 2 × 2.083 × 0.01147 × 10 = 0.4778 V, which is 1.991% of 24 V
4. For a limit of 3%, Lmax = 0.03 × 24 × 1.5 × 10⁻⁶ / (2 × 2.083 × 1.72 × 10⁻⁸) = 15.07 m

Worked example: a 72 W LED strip on 24 V, fed at one end with 5 m of 2.5 mm² copper

1. I = 72 / 24 = 3 A, and r = 1.72 × 10⁻⁸ / (2.5 × 10⁻⁶) = 0.00688 Ω/m
2. With the whole load at the far end, ΔV = 2 × 3 × 0.00688 × 5 = 0.2064 V
3. With the load spread evenly along the 5 m, ΔV = 0.1032 V

Drop for the 50 W fixture on 1.5 mm² copper at 24 V

Frequently asked questions

Why does low voltage lighting drop so much?

The same power needs a larger current at a lower voltage, and the drop grows with the current. A 12 V run drops twice the volts of a 24 V run for the same watts, which is four times the share.

What helps most?

A larger cross-section, a shorter run, or a higher supply voltage. Feeding a long strip from both ends or in sections also cuts the drop.

Does the drop matter for a constant-current driver?

The driver holds the current as long as its voltage range is not exceeded, so the drop between the driver and the LEDs only wastes power. The drop on the mains side of the driver is a different question.

Which resistivity should I use?

Use the value for the conductor temperature. The data sheet of the cable gives its resistance per kilometre, which is a little higher than the textbook value because of stranding.

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