Electric Potential Calculator

Solve electric potential using point charges or fields. See steps, units, and sign conventions clearly. Download CSV or PDF, then reuse your inputs later.

Choose the model that matches your scenario.
Positive or negative charge is allowed.
From charge to point of interest.
Quick check
If q is negative, potential is negative. Potential drops with larger r.
Result appears above this form after you calculate.

Example data table

Scenario Inputs Computed output
Point charge q = 2 µC, r = 0.50 m V ≈ 3.595e+04 V
Two charges (q₁= 1 µC, r₁=0.40 m), (q₂=-0.5 µC, r₂=0.20 m) V ≈ -1.123e+04 V
Uniform field E = 3 kV/m, d = 0.20 m, θ = 0° ΔV = -600 V
These examples assume vacuum/air using k ≈ 8.99×10⁹.

Formula used

Units: q in C, distances in m, E in V/m, and V in volts.

How to use this calculator

  1. Select a calculation mode that matches your setup.
  2. Enter values and choose units for each field.
  3. For multiple charges, add rows and keep distances positive.
  4. Press Calculate to view results above.
  5. Use the CSV/PDF buttons to export your latest result.
Note: This uses k for vacuum/air. Dielectric materials require adjusted permittivity.

Electric potential as energy per charge

Electric potential (V) expresses energy change per unit charge, measured in volts (J/C). In this calculator, a 2 µC source at 0.50 m produces about 3.60×104 V in vacuum/air using k≈8.99×109. Scaling is linear: doubling q doubles V, while doubling r halves V.

Point-charge model and distance sensitivity

The point-charge equation V=kq/r is highly distance-sensitive near the source. If q=1 µC, V is ~8.99×103 V at 1 m, but rises to ~8.99×104 V at 0.10 m. This is why small measurement errors in r can dominate the final value in short-range problems.

Superposition with multiple charges

When several charges influence one point, potentials add as scalars. For (q1=1 µC, r1=0.40 m) and (q2=−0.5 µC, r2=0.20 m), the contributions are +2.25×104 V and −2.25×104 V, giving a total near zero. The bar chart shows each contribution clearly before summing.

Uniform field potential difference

In a uniform field, the calculator uses ΔV=−E·d·cos(θ). With E=3 kV/m and d=0.20 m, moving parallel to E (θ=0°) yields −600 V, while moving opposite (θ=180°) yields +600 V. The graph sweeps θ from 0° to 180° to visualize sign changes.

Unit handling for reliable inputs

Real problems often mix units: charges in nC or µC and distances in cm or mm. This tool converts everything to C and m internally, then reports results in volts. For example, 500 nC equals 5.00×10−7 C, and 25 cm equals 0.25 m. Consistent units keep results comparable across modes.

Interpreting negative values and constraints

Negative potential typically indicates a negative source charge or motion with the field direction in ΔV calculations. Distances must be positive because r appears in the denominator. For materials other than air, replace k with 1/(4πϵ) using the medium’s permittivity, which reduces potential by the relative permittivity factor.

FAQs

1) What does the calculator output represent?

It returns electric potential V for point or multiple charges, or potential difference ΔV for a uniform field, all in volts with unit conversions applied.

2) Why can electric potential be negative?

Potential is proportional to charge sign. A negative charge gives negative V. In a uniform field, ΔV becomes negative when displacement is along the field direction.

3) Can I use centimeters and microcoulombs?

Yes. Select the appropriate units. The tool converts to meters and coulombs internally, then computes volts and displays consistent scientific formatting when needed.

4) What does the Plotly graph show?

Point-charge mode plots V versus r around your input distance. Multi-charge mode shows each charge’s voltage contribution. Field mode plots ΔV versus θ from 0° to 180°.

5) Does this include dielectric materials?

The default uses vacuum/air. For dielectrics, the effective constant becomes k/εr. You can approximate by dividing the displayed V or ΔV by the relative permittivity.

6) Why are zero or negative distances rejected?

Distance must be positive because the model contains division by r. A zero or negative value is non-physical here and would cause infinite or invalid outputs.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.