Coulomb Energy Calculator

Flexible Coulomb energy tool for students, labs, and engineers worldwide today online. Enter charges and distance, choose medium, then view energy, force, and potential.

Inputs

Signed value: positive or negative.
Use scientific notation if needed.
e = elementary charge.
Must be greater than zero.
Å = 10⁻¹⁰ m.
Typical water ~ 78.5 at room temperature.
0–12 recommended.

Formula used

The electrostatic potential energy between two point charges separated by distance r is:

U = (k / εr) · (q1 · q2) / r

How to use this calculator

  1. Enter q1 and q2 with the correct signs.
  2. Select a charge unit (C, mC, µC, nC, pC, or e).
  3. Enter the separation distance r and choose its unit.
  4. Set εr to 1 for vacuum, or another medium value.
  5. Click Calculate to view energy, force, and potential.
  6. Use Download CSV or Download PDF to save results.

Example data table

q1 (µC) q2 (µC) r (cm) εr U (J) Interpretation
2 3 5 1 ~1.08×10⁻² Repulsive
2 -3 5 1 ~-1.08×10⁻² Attractive
10 -10 1 2 ~-4.49×10⁻¹ Attractive (reduced by medium)
0.5 0.5 0.2 1 ~1.12×10⁻² Repulsive
Values are approximate, shown for learning and quick checks.

Professional article

1) What Coulomb energy represents

Coulomb energy is the electrostatic potential energy stored in the configuration of two point charges. It tells you how much work an external agent must do to bring charges from far apart to a separation r while moving slowly. The result is expressed in joules and can also be shown in electronvolts for microscopic scales.

2) Core equation and constants

The calculator uses U = (k/εr)(q1·q2)/r, where the Coulomb constant k ≈ 8.9875517923×10⁹ N·m²/C². In vacuum, this corresponds to k = 1/(4π ε0), with ε0 ≈ 8.8541878128×10⁻¹² F/m. These constants set the strength of electric interactions in SI units.

3) Unit handling and conversions

Charges are commonly entered in microcoulombs (µC) for lab problems, but the engine converts everything to coulombs internally. Distance can be meters, centimeters, millimeters, micrometers, nanometers, or angstroms (Å = 10⁻¹⁰ m). Accurate conversions matter because energy scales linearly with 1/r.

4) Role of dielectric media

Materials reduce electric interactions through the relative permittivity εr. The calculator applies k_eff = k/εr. For example, a medium with εr = 2 halves the energy and force compared with vacuum. Water is often modeled near εr ≈ 78.5 at room temperature, dramatically screening interactions.

5) Scaling with distance and charge

If you double both charges, energy increases by a factor of four because it depends on q1·q2. If you double the separation distance, energy is cut in half. The force output follows a steeper law, |F| ∝ 1/r², which is why nearby charges influence each other so strongly.

6) Sign conventions and physical meaning

A positive U indicates repulsion (same-sign charges), meaning you must supply work to bring them closer. A negative U indicates attraction (opposite-sign charges), meaning the system can release energy as the charges approach. The calculator labels the interaction type for quick interpretation.

7) Practical use cases and typical magnitudes

At macroscopic scales, even small charges can produce measurable energies. For instance, q1=2 µC, q2=3 µC, and r=5 cm gives about 1.08×10⁻² J. At atomic scales, electronvolt outputs are more convenient: a separation of 1 Å and charges near one elementary charge can yield energies on the order of electronvolts.

8) Common pitfalls and validation checks

Always confirm signs, units, and that r>0. If your answer looks off by powers of ten, the most common cause is mixing centimeters with meters or µC with C. A quick sanity check is to note that reducing r by 10 should increase |U| by 10 and |F| by 100.

FAQs

1) Can Coulomb energy be negative?

Yes. Opposite-sign charges produce negative potential energy, reflecting attraction and the possibility of releasing energy as the charges move closer.

2) What does εr change in the result?

It scales the interaction strength. Energy, force, and potential are all divided by εr, so higher εr means stronger screening and smaller outputs.

3) Why show results in eV as well?

Electronvolts are convenient for microscopic systems. When charges and distances are very small, joules become tiny, while eV stays readable.

4) Is the force direction included?

The calculator reports force magnitude. Direction depends on charge signs: same-sign charges repel and opposite-sign charges attract along the line joining them.

5) Does this apply to extended objects?

This model assumes point charges. For extended charge distributions, you typically integrate contributions or approximate with effective point charges when far away.

6) What units should I use for laboratory problems?

µC for charge and cm for distance are common in labs. The calculator converts to SI internally, so any supported unit set is fine.

7) How do I check if my output is reasonable?

Vary one input at a time. Energy should scale with q1·q2 and 1/r, while force should scale with q1·q2 and 1/r².

Use results to compare interactions across different scales safely.

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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.