Electricity & Magnetism
Resistance
Resistance of a wire depends on geometry and material.
Variables
RΩ
Resistance
Electrical resistance
In SI units: kg·m²/(A²·s³)
Allowed values: 0 or more
ρΩ·m
Resistivity
Material property
In SI units: kg·m³/(A²·s³)
Allowed values: 0 or more
Lm
Length
Wire length
Allowed values: greater than 0
Am²
Cross-sectional area
Wire area
Allowed values: greater than 0
Derivation
R = ρL/A from microscopic Ohm's law.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- ρ = 2 Ω·m (Resistivity)
- L = 3 m (Length)
- A = 4 m² (Cross-sectional area)
Result: R = 1.5 Ω
Other electricity & magnetism formulas with the same quantities
- Electric Power (Electric Circuits) shares Resistance
- RC Time Constant (Capacitance) shares Resistance
- RL Time Constant (Electromagnetic Induction) shares Resistance
- Impedance (RLC Series) (AC Circuits) shares Resistance
Where this formula is listed
- Electricity & Magnetism formulas, under Electric Circuits, alongside Electric Current, Resistors in Series, Resistors in Parallel, Kirchhoff's Voltage Law and Kirchhoff's Current Law.
- In the electricity & magnetism list it comes after Electric Current and before Resistors in Series.
- Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Resistance formula?
Resistance is written R = ρL/A. Resistance of a wire depends on geometry and material. It belongs to Electricity & Magnetism, under Electric Circuits.
What are the units in R = ρL/A?
In SI units, R is resistance, measured in kg·m²/(A²·s³); ρ is resistivity, measured in kg·m³/(A²·s³); L is length, measured in m; A is cross-sectional area, measured in m².
How is the Resistance formula derived?
R = ρL/A from microscopic Ohm's law. The result is R = ρL/A.