Point Charge Electric Field Calculator
Compute the electric field produced by one point charge: E = k·Q / r² with k = 8.9875517923 × 10⁹ N·m²/C² (CODATA 2018). Runs entirely in your browser — no server, no sign-up.
Q may be negative (e.g. −5 µC). The sign of Q determines field direction: positive = away from the charge, negative = toward the charge.
Three charges on one straight line. Enter each charge’s value + position (x in meters), then set the test point where the net field is computed. Unlike the #1570 superposition which computes force on the middle charge, here the field at the test point is computed — no need to place a test charge.
Formula
with k = 8.9875517923 × 10⁹ N·m²/C² (Coulomb constant, CODATA 2018; k = 1/(4πε₀)) and εᵣ = relative permittivity of the medium (1 for vacuum). E is signed: positive means the field points away from the charge (Q > 0), negative means toward the charge (Q < 0). N/C units are identical to V/m.
Worked examples
Example 1 (find E). Q = 1 µC, r = 10 cm (vacuum):
E = 8.9875517923 × 10⁹ × 1×10⁻⁶ ÷ (0.1)² = 898,755.18 N/C, pointing away from the charge (positive Q).
Example 2 (find Q). Given E = 500 N/C at r = 20 cm:
Q = E·r²/k = 500 × (0.2)² / 8.9875517923×10^9 = 2.22530 × 10⁻⁹ C = 2.2253 nC.
Example 3 (find r). Q = 2 µC, desired E = 1,000 N/C:
r = √(k·|Q|/E) = √(8.9875517923×10^9 × 2×10^-6 / 1000) = 4.240 m.
Example 4 (superposition). q₁ = +2 µC at x = 0 m, q₂ = −1 µC at x = 0.5 m, test point at x = 1 m:
E₁ = 17,975.10 N/C, E₂ = -35,950.21 N/C, so E_net = -1.79751 × 10⁴ N/C — field points toward −x.
Unit reference
| Charge unit | Value in coulombs |
|---|---|
| coulomb (C) | 1 |
| millicoulomb (mC) | 10^-3 |
| microcoulomb (µC) | 10^-6 |
| nanocoulomb (nC) | 10^-9 |
| picocoulomb (pC) | 10^-12 |
Frequently asked questions
What is the electric field formula for a point charge?
E = k·Q ÷ r², with k = 8.9875517923 × 10⁹ N·m²/C² (CODATA 2018), Q = source charge in coulombs, and r = distance from the charge in meters. Field E is expressed in newtons per coulomb (N/C), identical to volts per meter (V/m). Example: Q = 1 µC at 10 cm gives E = 898,755.18 N/C.
How does this calculator differ from the Coulomb’s law calculator (#1570)?
This calculator (#1603) computes the ELECTRIC FIELD E (N/C) produced by ONE source charge at a point in space, with no second charge needed. The Coulomb’s law calculator (#1570) computes the Coulomb FORCE F (N) between TWO charges. Relation: E = F ÷ q, with q = test charge. For the force between two charges, use Coulomb’s law calculator.
Which way does a point charge’s electric field point?
The electric field direction is radial: AWAY from the charge when Q is positive (a positive test charge is repelled), and TOWARD the charge when Q is negative (a positive test charge is attracted). This calculator shows the direction automatically based on the sign of Q.
What units are supported?
Charge: C, mC, µC, nC, pC. Distance: m, cm, mm, km. Electric field: N/C (equivalent to V/m). You can also choose the medium: vacuum (εᵣ = 1), air (εᵣ ≈ 1.0006), or your own εᵣ value.
How does the 1D superposition mode work?
For 2–3 collinear charges, the calculator computes the field from each charge at the test point (Eᵢ = k·qᵢ × d ÷ (εᵣ·|d|³), with d = x_test − x_charge) then sums them: E_net = E₁ + E₂ + E₃. A positive sign means the field points toward +x, negative toward −x. Example: +2 µC at x = 0 and −1 µC at x = 0.5 m give E₁ = 17,975.10 N/C, E₂ = -35,950.21 N/C, so E_net = -1.79751 × 10⁴ N/C (pointing toward −x).
Is electric field the same as electric potential?
No. Electric field E (N/C) is force per unit charge; electric potential V (volts) is energy per unit charge. For a point charge they relate as: V = k·Q ÷ (εᵣ·r) and E = −dV÷dr. This calculator shows both: the main field and the potential at the test point as extra info.
See also
Coulomb’s Law Calculator — force F (N) between TWO charges; relation to this tool: E = F ÷ q.
Electric Charge Converter — charge unit conversion (C, mC, µC, nC, pC, Ah, mAh).
Scope limits: this tool is purely point-charge electrostatics (field from one source charge). For the force between two charges use coulombs-law; for unit conversion use charge-converter.
Free tool by NRTechStudio