Electric Field Calculator
Calculate electric field strength from point charges, force and charge, voltage between plates, or multiple charge vectors with direction and unit conversions.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the electric field model, then choose the unknown variable.
Enter the known values
Fill in the visible fields. The Electric Field Calculator updates automatically.
Enter the active known values and units. Valid results update automatically, and Calculate performs a full validation check.
Solution
Live result, direction, quick checks, assumptions, and full equation walkthrough.
Quick checks
- Equivalent field—
- Direction—
- Model—
- Medium—
Show solution steps See conversions, equation substitution, assumptions, and interpretation
- Enter values to see the full solution steps and checks.
Electric field visual
The diagram updates to match the selected calculation method and sign convention.
Method, Sources, and Assumptions
Electrostatics relationships, active medium assumptions, limitations, and interpretation guidance.
Uses standard Coulomb-law, force-per-charge, parallel-plate, and vector-superposition relationships for educational physics and electrical engineering calculations.
- Coulomb constant: k = 8.9875517923 × 10^9 N·m²/C².
- Point-charge and vector modes assume ideal point charges and static fields.
- Parallel-plate mode assumes a uniform field and neglects edge fringing.
Calculator guide
What the Electric Field Calculator Determines
The Electric Field Calculator solves common electrostatics problems from four starting points: a single point charge, force on a test charge, voltage across ideal parallel plates, or the vector sum from multiple point charges. Depending on the selected method, it can solve for electric field, charge, distance, force, voltage, plate spacing, or a net 2D field with direction.
Electric field is a vector quantity that describes the force a positive test charge would experience per unit charge at a location. The most important first step is choosing the physical model that matches the information you actually know.
- Point charge
- Charge and distance using an inverse-square field model
- Field units
- N/C and V/m describe the same physical field quantity
- Vector mode
- Up to three signed point charges with x-y coordinates
How to Use the Calculator
Select the model first, then choose the unknown. The calculator changes the visible inputs so you only enter quantities required by that physical relationship.
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Choose the calculation method
Use Point Charge for a field created by one charge at a known distance, Force and Test Charge when force and charge are known, Parallel Plates for an ideal uniform plate field, or Net Field from Multiple Charges for a 2D superposition problem.
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Select what to solve for
Choose the missing quantity in the Solve For control. The calculator hides the unknown and keeps the required known values visible.
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Enter values in their actual units
Use the unit selector beside each input rather than converting by memory. This is especially important for microcoulombs, nanocoulombs, millimeters, and centimeters, where a missed prefix can change the result by orders of magnitude.
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Set the medium only when it belongs in the model
The Advanced Options include relative permittivity for the point-charge and multiple-charge calculations. Use a custom value only when the simplified homogeneous-medium assumption is appropriate for the problem.
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Check direction and the solution steps
Review the result, direction statement, model label, and full calculation steps. In vector mode, confirm the x-y coordinate system and observation point before trusting the resultant angle.
Electric Field Equations Used
The calculator does not force every problem into one formula. It selects the electrostatic relationship that matches the chosen method and converts entered quantities to consistent base units before solving.
Point charge field
Electric field magnitude increases directly with source-charge magnitude and decreases with the square of distance. The calculator uses the sign of the source charge to interpret direction.
Field from force on a test charge
Electric field is force per unit test charge. For magnitudes, \(E=|F|/|q|\). A negative test charge experiences force opposite the electric-field direction.
Ideal parallel plates
For an approximately uniform field between large parallel plates, field magnitude equals voltage difference divided by plate spacing. This approximation is best away from plate edges.
Multiple point charges in 2D
Each charge contributes an electric-field vector at the observation point. The calculator resolves the contributions into x and y components, adds those components, then reports net magnitude and direction.
- \(E\)
- Electric field magnitude, commonly expressed in N/C or V/m.
- \(Q\)
- Source charge creating the electric field in point-charge mode.
- \(q\)
- Test charge experiencing electric force in the force-and-charge relationship.
- \(r\)
- Distance from the source charge to the observation point; it must be greater than zero.
- \(k\)
- Coulomb constant used in the point-charge relationship.
- \(\varepsilon_r\)
- Relative permittivity used by the calculator’s simplified homogeneous-medium option.
Worked Example: Point Charge Field
Find the electric field magnitude 20 cm from a positive 3.0 μC point charge with relative permittivity set to 1.
Convert the units
Substitute the values
Result
\(E\approx6.74\times10^5\ \text{N/C}\)
Because the source charge is positive, the electric field points radially away from the charge. The same magnitude can also be written as approximately \(6.74\times10^5\ \text{V/m}\).
How to Interpret Electric Field Results
The numerical field strength tells you how strongly a positive test charge would be pushed per unit charge at the observation point. Direction, geometry, and the selected model determine what that number means physically.
Point-charge distance is squared
Holding charge and relative permittivity constant, doubling distance reduces the field to one quarter; halving distance makes the field four times larger.
Parallel-plate field scales with V/d
Holding plate spacing constant, doubling voltage doubles the ideal field. Holding voltage constant, doubling spacing halves the ideal field.
Vector cancellation is possible
Two large field contributions can partially or completely cancel at an observation point. A small net field does not necessarily mean each individual charge creates a weak field.
Units, Direction, and Input Quality
Electric-field calculations are short, but prefixes and sign conventions can change the result dramatically. Keep the entered number paired with the unit shown beside it.
- \(1\ \mu\text{C}=10^{-6}\ \text{C}\), while \(1\ \text{nC}=10^{-9}\ \text{C}\).
- \(1\ \text{cm}=10^{-2}\ \text{m}\) and \(1\ \text{mm}=10^{-3}\ \text{m}\).
- For point charges, a distance conversion error is squared by the \(1/r^2\) relationship.
- Distance or plate spacing must be greater than zero for these closed-form models.
Common Electric Field Calculator Mistakes
The most consequential errors usually come from choosing the wrong physical model, mixing source and test charge, or ignoring direction—not from the final arithmetic.
Confusing source charge Q with test charge q
The source charge creates the point-charge field. A test charge is used to relate an already-existing field to electric force through \(\vec{F}=q\vec{E}\).
Entering μC as C
A value of 5 μC is \(5\times10^{-6}\) C, not 5 C. Use the calculator’s charge-unit selector rather than changing the number without changing its unit.
Using distance instead of distance squared
The point-charge model is inverse-square. A distance mistake therefore has a larger effect than a simple linear scaling error.
Adding fields as scalars
Electric fields from multiple charges must be added as vectors. Opposing x or y components can cancel even when the individual magnitudes are large.
Treating E = V/d as universally exact
The plate relationship assumes an approximately uniform field. Near finite plate edges, fringing makes the field nonuniform.
Using a dielectric correction outside its simple model
A single relative-permittivity value represents a homogeneous simplified medium. Real interfaces, conductor boundaries, layered materials, and complex geometry can require a field solution rather than a scalar correction.
Assumptions, Limits, and Sources
The calculator uses standard closed-form electrostatics relationships. They are exact for the ideal mathematical models being applied, but real hardware may depart from those models because of geometry, boundaries, materials, and time-varying effects.
Point-charge approximation
The source is modeled as a point charge. An extended charge distribution may require integration or a different field model.
Electrostatic assumption
The formulas describe static electric-field relationships. Rapidly time-varying electromagnetic systems require the broader Maxwell-equation framework.
Parallel-plate approximation
The \(E=|\Delta V|/d\) mode represents an approximately uniform central field between plates and does not resolve fringing near edges.
Homogeneous-medium simplification
The relative-permittivity option assumes a single effective medium. Interfaces and nonuniform dielectric geometry can redistribute the field.