Resistance Calculator
Resistance from geometry: R = ρL/A on your own wire — material, length, gauge — with the voltage drop the run eats priced live and the superconductor case refused.
Resistance Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Room-temperature resistivity; hot wire runs higher
- Uniform circular section, DC reading
In short: A 100 m run of 2.05 mm copper wire (ρ ≈ 1.68×10⁻⁸ Ω·m, approximate): section π·d²/4 = 3.300636×10⁻⁶ m², so R = ρL/A = 0.508993 Ω. The drop card prices the run at a 20 A load: 10.179857 V eaten by the walls — 8.483214% of a 120 V supply warms the house's bones, not its lamps. The geometry card doubles the walk: 200 m doubles R to 1.017986 Ω, and halving the wire diameter QUADRUPLES the ohms — proportionality twice over. Two such runs in parallel carry R/2 = 0.254496 Ω. Ask for zero resistivity and the page refuses: that is a superconductor, and this page prices ordinary conductors.
Formula
R = ρ·L / A, A = π·d²/4 · drop = I·R · parallel: conductances add
Resistance is the geometry of opposition: resistivity is the material's price per metre-per-area, and the wire's shape multiplies it. Long and thin is expensive; short and fat is cheap — proportionally, twice over. The voltage-drop card turns the ohms into the tax a real run takes out of the supply, which is why wire gauges exist.
Worked Example
- Pick the material's resistivity, or enter your own.
- Enter the run length and the wire diameter.
- Read R, then the drop card at a 20 A load.
- Use the geometry card before shortening runs or up-sizing wire — the lever is proportional, both ways.
Defaults: 0.508993 Ω; drop 10.179857 V at 20 A (8.483214% of 120 V); 200 m doubles it; parallel two = 0.254496 Ω.
Strengths & Limits Of This Model
Where this engine is strong
- Drop card prices the run at a real load
- Superconductor case refused by name
Where it stops
- No skin effect or AC gauging
- No temperature coefficient pricing
Practical Use Cases
Wiring
voltage drop before the lamps dim
Heater design
nichrome lengths that land on a wattage
Teaching
why gauges and short runs matter
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Resistance Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the difference between resistance and resistivity?
Resistivity ρ belongs to the MATERIAL — ohms times metres, the price per unit cell of wire. Resistance R belongs to the PIECE: the material's price multiplied by length and divided by section. Copper is a cheap material; a long thin copper wire is still an expensive piece, and the page computes exactly how expensive.
Why does halving the diameter quadruple R?
The section is π·d²/4 — it grows with the SQUARE of the diameter, so half the diameter is a quarter of the section, and R divides by A: four times the ohms. The card computes both directions so the lever is a number you watched move, not a remembered square.
What does the drop card price?
The tax of the run: at a 20 A load the wire eats I·R volts before the load sees any. On the defaults that is 10.179857 V — about 8.483214% of a 120 V supply — which is why long runs demand thicker wire, and why the drop is budgeted, not discovered.
Why is ρ = 0 refused?
Because a resistivity of zero is a superconductor, and the page prices ordinary conductors: its cards assume the material charges for the walk. Real superconductors bring critical currents and cryogenics — a different, colder subject.
Should the return path count in L?
For a circuit, yes: the current walks there AND back, so the drop card's run is the full loop. The geometry law does not care which metre the ohms live on; your drop budget does — count both legs.
Why does nichrome appear in the chips?
As the heater wire: at about 1.1×10⁻⁶ Ω·m it is some 65× copper's price, which is how a coiled few metres of it lands on a useful wattage. Swap the chip and watch the same geometry become a heating element instead of a cord.
How do two runs in parallel behave?
Conductances add: two identical runs carry R/2, and the general case is the reciprocal law. That is parallel wiring's whole gift — and why panels parallel feeders when the drop budget cannot be met with one gauge.
How does temperature change all this?
Twice over: the wire's geometry grows (the thermal expansion page's millimetres) and copper's resistivity itself climbs about 0.4% per kelvin near room temperature — the bigger effect. A hot motor draws differently from a cold one; the page's numbers are the cold, honest baseline.