Electric Potential Calculator
Compute the electric potential of point charges V = kQ/r in all directions (solve for V, Q, or r — ± signs automatic), potential energy U = qV, potential difference ΔV & work W = qΔV, and superposition of many charges. Constant k = 8.9875517923x10^9 N·m²/C² (CODATA 2018). Runs 100% in your browser.
Limits of this tool (read first)
#1604 = potensial V (volt, skalar) & potential energy U = qV (joule).
#1603 = field E (N/C, vektor).
#1570 = force F (newton).
Hubungan ketiganya: E = −∇V, U = qV, F = qE.
See also: Point-Charge Electric Field Calculator (#1603) · Coulomb’s Law Calculator — Force (#1570) · Konverter Volt ↔ eV (#1491)
Add up to 8 source charges. Optional: enter a test charge q to compute the potential energy U = q·Vtotal.
Verified example
Point charge Q = 1 µC, distance r = 0.1 m (10 cm):
V = k × Q / r = 8,9875517923x10^9 × 10^-6 / 0,1 = 89.875,517923 V ≈ 89,88 kV.
Field magnitude at that point (info): E = kQ/r² = 8.987551792x10^5 V/m.
Potential energy of a q = 1 nC test charge at that point:
U = qV = 10^-9 × 89.875,517923 = 8,987551792x10^-5 J ≈ 89,875517923 µJ ≈ 5,609588607x10^14 eV.
Negative charge: Q = −2 µC at r = 5 cm → V = -359,502.071692 V ≈ -359.50 kV (negative — the field does work).
Potential difference & work: V1 = 100 V → V2 = 250 V, q = 2 nC → ΔV = 150 V, W = qΔV = 3x10^-7 J = 300 nJ.
Superposisi: +1 µC at 10 cm and −1 µC at 20 cm → V_total = 44,937.7589615 V ≈ 44.94 kV.
All numbers above were independently recomputed (50-digit precision) and match the calculator engine above — reproduce them yourself in Modes 1–4.
Frequently asked questions (FAQ)
What is electric potential (V)?
Electric potential V at a point is the work per unit charge required to bring a positive test charge from infinity (the V = 0 reference point) to that point without acceleration. For a single point charge Q at distance r, V = k × Q / r, with k = 8.9875517923x10^9 N·m²/C². Its unit is the volt (V); 1 volt = 1 joule per coulomb.
What is the difference between potential V, potential energy U, field E, and force F?
They are related but distinct quantities: potential V (volts) is a SCALAR — computed by this calculator (#1604 electric-potential) together with potential energy U = qV (joules). Electric field E (N/C) is a VECTOR — computed by #1603 electric-field-of-a-point-charge. Electrostatic force F (newtons) — computed by #1570 coulombs-law. They are linked by E = −∇V (the field is the negative gradient of the potential), U = qV, and F = qE.
Why can electric potential be negative?
Because V = kQ/r follows the sign of the source charge Q. A positive charge produces positive V (external work is needed to bring a positive test charge closer); a negative charge produces negative V — meaning the field itself does work as a positive test charge is brought closer, and work is needed to move it away. This calculator handles the ± sign automatically in every mode.
Example: a 1 µC charge at 10 cm — what is the potential?
V = k × Q / r = 8.9875517923x10^9 × 10^-6 / 0.1 = 89,875.517923 V ≈ 89.88 kV. Potential energy of a 1 nC test charge at that point: U = qV = 10^-9 × 89,875.517923 = 8.987551792x10^-5 J ≈ 89.88 µJ ≈ 5.609588607x10^14 eV. This example is verified and you can reproduce it in Mode 1 and Mode 2.
What is the electron-volt (eV)?
The electron-volt is a unit of energy: the energy gained by one elementary charge (e = 1.602176634x10^-19 C) crossing a potential difference of 1 volt. 1 eV = 1.602176634x10^-19 J (exact, 2019 SI definition). This calculator also shows the energy result U in eV — handy at atomic scales. For volt↔eV conversion with charge number z (particle physics), see the volts-to-ev calculator.
How do you calculate the work of moving a charge (W = qΔV)?
First compute the potential difference ΔV = V2 − V1, then W = q × ΔV. Example: V1 = 100 V, V2 = 250 V, q = 2 nC → ΔV = 150 V and W = 2x10^-9 × 150 = 3x10^-7 J = 300 nJ. Positive W means an external agent must do work (against the field); negative W means the field does the work. Use Mode 3 — it can also be reversed to solve for q or ΔV.
How are the potentials of several charges combined (superposition)?
Potential is a scalar, so the total is just the algebraic sum: V_total = V1 + V2 + … = kQ1/r1 + kQ2/r2 + … — the ± signs are summed as well, unlike field vectors which need directions. Example: +1 µC at 10 cm (V = +89,875.517923 V) and −1 µC at 20 cm (V = −44,937.7589615 V) → V_total = 44,937.7589615 V ≈ 44.94 kV. Mode 4 computes up to 8 charges at once.
Can the potential be zero even when charges are nearby?
Yes. Because the summation is scalar, positive and negative contributions can cancel out. Classic example: at the midpoint between symmetric +Q and −Q charges, V_total = kQ/r + k(−Q)/r = 0 — while the electric field at that point is actually at its maximum. That is why potential and field are different quantities.
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