Resistance of a uniform wire is set by the material's resistivity and the wire's shape — R = ρL/A: proportional to length, inversely proportional to cross-sectional area. This free calculator solves for the resistance, the resistivity, the length or the area, in any unit, and shows every step of the working.
Every wire resists the flow of charge, and how much it resists is fixed by two things: what it is made of and what shape it is. The material contributes its resistivity ρ (in ohm-metres), an intrinsic property; the shape contributes the length L and the cross-sectional area A. Put them together and you get the resistance: R = ρL/A. A longer wire has more material for charge to fight through, so R rises with L; a fatter wire gives charge more room, so R falls as A grows.
There are three steps. First, decide what you want — the resistance R, or one of ρ, L or A — and pick it in the calculator's Solve for menu. Second, enter the values you know: resistivity in Ω·m, length in metres, and area in square millimetres or square metres. The most important conversion happens here — an area given in mm² is multiplied by 10-6 to reach m², and the calculator does this automatically when you choose the mm² unit. Third, read the answer to three significant figures with the worked steps, and, when solving for R, the conductance G = 1/R in siemens. The four rearrangements are R = ρL/A, ρ = RA/L, L = RA/ρ and A = ρL/R.
Two relationships are worth feeling directly. Resistance is proportional to length — double the wire and you double R — but inversely proportional to area, so doubling the cross-section halves R, and doubling the diameter quarters it (area goes as diameter squared). Resistivity itself spans an enormous range, from about 1.6×10-8 Ω·m for silver and copper to roughly 1.1×10-6 Ω·m for nichrome — about sixty-five times higher — which is why heating elements are wound from nichrome and power cables from copper. Once you have the resistance, the current it draws follows from the Ohm's Law calculator (V = I·R); to combine several resistors, see the resistor calculator, or look up a term in the physics glossary.
A copper wire has resistivity ρ = 1.68×10-8 Ω·m, length L = 2.0 m and cross-sectional area A = 1.0 mm². Converting the area to SI, A = 1.0×10-6 m², the resistance is R = ρL/A = (1.68×10-8 × 2.0) / (1.0×10-6) = 0.0336 Ω, and the conductance is G = 1/R ≈ 29.8 S. Double the length to 4.0 m and R doubles to 0.0672 Ω; double the area to 2.0 mm² instead and R halves to 0.0168 Ω — the proportional and inverse relationships in action.
Resistivity and R = ρL/A underpin cable sizing and voltage-drop calculations in wiring, the design of heating elements and fuses, strain gauges and resistance thermometers, the trace widths on printed circuit boards, and the choice of conductor in everything from earbuds to national grids. Whenever an engineer picks a wire gauge or a material, this is the equation behind the decision.
Because resistivity is defined in SI units of ohm-metres, so R = ρL/A only gives ohms when every quantity is in base SI: resistivity in Ω·m, length in metres and area in square metres. A cross-section quoted in mm² must be multiplied by one millionth to become m² (1 mm² = 0.000001 m²). Forgetting this factor is the single most common error and makes the resistance a million times too small; the calculator does the conversion for you when you pick mm².
Resistivity ρ is a property of the material alone — copper has the same resistivity whether it is a thin wire or a thick bus-bar. Resistance R is a property of a particular object, depending on the material and its shape through R = ρL/A. Two wires of the same metal can have very different resistances if their length or thickness differs, but they share one resistivity.
Because resistance depends on cross-sectional area, not diameter, and area grows with the square of the diameter (A = pi·d²/4). Doubling the diameter multiplies the area by four, and since R is inversely proportional to area, the resistance drops to a quarter. This is why thick cables carry heavy currents with little loss — a small increase in diameter buys a large drop in resistance.
Set the “Solve for” menu to ρ (resistivity), then enter the measured resistance R, the sample length L and its cross-sectional area A. The calculator applies ρ = R·A/L and returns the resistivity in Ω·m. This is exactly how resistivity is measured in the lab: pass a known current through a uniform sample, read the voltage to get R, and divide by the geometry factor L/A.
This calculator uses the room-temperature resistivity you enter and computes the geometric resistance R = ρL/A. Resistivity itself rises with temperature for metals, roughly as rho(T) = rho20 · (1 + alpha·(T - 20)); to see that effect interactively, and to switch between metals, use the resistance simulator, then feed the temperature-corrected resistivity back into this calculator if you need a precise number.