electric field and potential formulas and interpretation
A point charge produces both an electric field and an electric potential around it.
The calculator preserves charge and distance unit conversion with separate field and potential results.
How to use the electric field and potential calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Field decreases with distance squared, while potential decreases with distance.
E = kq/r²; V = kq/r- E — Electric field
- Force per unit positive charge (N/C)
- V — Electric potential
- Potential energy per charge (V)
- q — Source charge
- Point charge (C)
- r — Distance
- Distance from charge (m)
Point-charge example
Find the field and potential 0.1 m from a 1 μC charge.
- Charge
- 1 μC
- Distance
- 0.1 m
- E = kq/r² ≈ 8.99 × 10⁵ N/C
- V = kq/r ≈ 89,900 V
Result: Field is about 899 kN/C and potential about 89.9 kV.
Signs follow the source charge; the displayed field direction is radial.
Understanding your results
Interpreting the result
The point-charge approximation is best when source dimensions are small relative to distance.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.