The electric field calculator above handles the three questions people actually bring to this topic. Given a charge and a distance, what is the field there? Given a field and a charge sitting in it, what force does that charge feel? And given two parallel plates at a known voltage, what uniform field exists between them? Those are three different equations, and this tool keeps them separate rather than fusing them into one input box that quietly assumes which case you meant.
Arb Digital builds free calculators that carry their constants from an authoritative source rather than from memory. The Coulomb constant used here is derived from the CODATA value of the vacuum electric permittivity rather than being hard-coded as a rounded figure, so the results agree with published values to full precision. This page also states the boundary against the converters already on the site: a converter rescales a quantity between units, while this derives field strength, potential and force from formulas.
What This Electric Field Calculator Does
In point-charge mode it computes the magnitude of the electric field at a chosen distance from a single charge, using Coulomb's law in field form. The hero shows the field in newtons per coulomb, which is identical to volts per metre. The grid adds the electric potential at that same point, the force the field would exert on the test charge you entered, the source charge expressed as a count of elementary charges, and the field at twice the distance — a direct demonstration of the inverse-square law.
In force mode you supply a field strength and a charge, and the tool returns the force on that charge. This is the definition of the electric field turned around: the field is defined as force per unit charge, so multiplying gives the force back. The direction follows the field for a positive charge and opposes it for a negative one, which is why the sign of the charge matters and the tool reports it.
In parallel-plate mode it computes the uniform field between two plates from the voltage across them and their separation. This is the geometry inside capacitors, cathode-ray tubes, electrophoresis gels and ink-jet deflection heads, and it is by far the easiest field to create deliberately, because it depends only on two numbers you control directly.
How to Use It
- Pick the mode first. The three cases read different input fields, and the hero label changes to tell you which quantity is being reported.
- Enter the charge with its unit. Real laboratory charges are microcoulombs and smaller — a coulomb is an enormous amount of static charge. The unit dropdown saves you writing exponents by hand.
- Set the relative permittivity if the charge is not in air. Vacuum and air are both effectively 1. Immersing the same charge in water divides the field by roughly 80.
- Check the distance carefully. Field strength depends on the square of distance, so a factor-of-two error in distance is a factor-of-four error in the answer.
- Read the grid, not only the hero. Potential and field answer different questions, and confusing them is the most common conceptual error in this topic.
The Formula: How Field Strength Is Calculated
The electric field of a point charge has magnitude E = kQ ÷ (εrr2), where k = 1 ÷ (4πε0). OpenStax University Physics Volume 2, section 5.4 on the electric field, defines the field through the relation F = QE and gives the point-charge field in exactly this inverse-square form.
The constant comes from the permittivity of free space. NIST's CODATA value for the vacuum electric permittivity is 8.8541878188 × 10−12 F/m, and dividing one by four pi times that figure gives a Coulomb constant of approximately 8.9876 × 109 N m2/C2. This calculator computes k from the permittivity at run time rather than storing a rounded value. The elementary-charge figure used to express your charge as a count of electrons comes from the same source: NIST gives the elementary charge as exactly 1.602176634 × 10−19 C.
Work the defaults. A charge of 1 µC in air at 0.05 m gives E = 8.9876 × 109 × 10−6 ÷ 0.0025 = 3.595 × 106 N/C. The potential at the same point is V = kQ ÷ r = 8.9876 × 109 × 10−6 ÷ 0.05 = 1.798 × 105 V. A 1 µC test charge placed there feels a force of 3.595 N, which is roughly the weight of a 370 g object — a surprisingly large force for two specks of charge, and a good illustration of how strong the electrostatic interaction is.
Field and Potential Are Not the Same Thing
Both numbers appear in the results, and confusing them is the single most common error in electrostatics. The field is a vector with units of newtons per coulomb; the potential is a scalar with units of volts. They are related — the field is the negative gradient of the potential — but they behave differently with distance. Around a point charge the field falls as one over distance squared while the potential falls as one over distance.
That difference has a consequence people often find counter-intuitive: the field can be zero somewhere the potential is not, and the potential can be zero somewhere the field is not. Midway between two equal and opposite charges, the potential is zero because the two contributions cancel as signed scalars, yet the field is strong because the two contributions point the same way and add as vectors. Exactly at the midpoint between two equal like charges the reverse happens: the field cancels while the potential is at a local minimum but not zero.
The practical rule is that potential tells you about energy and field tells you about force. If you are asking how much work it takes to move a charge from A to B, you want potential difference. If you are asking which way something accelerates and how hard, you want the field.
Superposition: Why One Charge Is Rarely the Whole Story
This tool computes the field of a single point charge. Real situations almost always involve several. The rule for combining them is superposition: compute the field from each charge independently, then add the results as vectors. That means magnitudes cannot simply be added unless the fields happen to point the same way.
For charges along a straight line the vector addition collapses to signed addition, which is easy enough to do by hand from repeated runs of this calculator. For charges in a plane you need to resolve each field into components before adding. Note also that superposition is exact, not an approximation — the equations of electrostatics are linear, so adding solutions gives a solution. That is a stronger guarantee than most physical models offer.
Parallel Plates and Why the Field Is Uniform
Between two large parallel plates held at a voltage difference, the field is E = V ÷ d and it is the same everywhere in the gap. That uniformity is what makes the geometry so useful. With 500 V across a 1 cm gap the field is 50,000 V/m, and a charge placed anywhere between the plates feels the same force regardless of position.
Two limits are worth knowing. The uniformity holds only well away from the plate edges, where fringing fields curve outward and the simple formula fails. And air breaks down at around three million volts per metre, so a 1 cm gap cannot hold much more than about 30 kV before it arcs. The tool will happily compute a field above breakdown because the arithmetic is still valid — it just would not exist in air. If you are working with capacitors, our capacitance converter handles farad-scale unit changes.
What Counts as a Strong Field
Numbers in electrostatics span an enormous range, and it helps to have anchors. Fair-weather atmospheric field at ground level is on the order of a hundred volts per metre. The field just outside a charged plastic comb is a few thousand. Dry air breaks down at roughly three million volts per metre, which is the ceiling for anything you can build in open air without arcing. Inside a thin capacitor dielectric, fields of tens or hundreds of millions of volts per metre are routine, because a solid insulator tolerates far more than air does.
At the atomic scale the numbers climb again. The field an electron experiences at the first Bohr radius of a hydrogen atom is of the order of ten to the eleventh volts per metre, which is why atomic binding is untouched by any laboratory field you could apply externally. The preset button on this page sets exactly that geometry so you can see the figure emerge from the same formula that handles a charged sphere on a bench.
The point of these anchors is calibration. If a calculation returns a field of ten to the fifteenth volts per metre for a hand-sized object, something is wrong with the inputs — most often a distance entered in centimetres while the tool expected metres. Sanity-checking against a known range catches that class of error faster than re-reading the arithmetic.
How This Differs From the Converters and Coulomb's Law
The boundary is worth stating in one sentence: a converter rescales a quantity between units, while this calculator derives field strength, potential and force from formulas. The electric charge converter turns coulombs into microcoulombs or elementary charges; it cannot tell you what field that charge produces. The magnetic field converter does the same job for teslas and gauss, and magnetic fields are a separate phenomenon from the electric fields on this page.
The nearest calculator is the Coulomb's law calculator, which computes the force between two specified point charges. This page computes the field a single charge creates at a point in space, whether or not anything is there to feel it. The two are the same physics viewed differently: field is force per unit charge, so Coulomb's law is what you get when you place a second charge in the field this tool reports. If your problem names two charges, use Coulomb's law; if it asks about a point in space, use this.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Confusing field with potential — one is a vector in newtons per coulomb, the other a scalar in volts, and they fall off with distance at different rates.
- Adding field magnitudes instead of vectors — superposition adds directions too, so two fields of equal size can sum to anything from double to zero.
- Forgetting the medium — a charge in water produces a field roughly eighty times weaker than the same charge in air, because the relative permittivity divides the result.
- Using the plate formula near the edges — fringing fields curve out beyond the plate boundary and the uniform-field assumption stops holding there.
- Ignoring the sign of the charge — magnitude alone does not tell you which way a charge will move, and direction is usually the point of the question.
Related Free Tools From Arb Digital
Convert charge units before or after a calculation with the electric charge converter, and handle very large or very small results with the scientific notation converter. For force between two named charges use the Coulomb's law calculator. Circuit work is covered by the electrical power calculator, the capacitance converter and the LC resonant frequency calculator, while the magnetic field converter covers the magnetic side. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
Newtons per coulomb, which is exactly the same unit as volts per metre. The two forms are interchangeable, and which one you see depends on whether the field is being described as force per unit charge or as a potential gradient.
It computes the constant at run time as one divided by four pi times the permittivity of free space, using the CODATA value of 8.8541878188 times ten to the minus twelve farads per metre. That gives approximately 8.9876 times ten to the ninth newton metres squared per coulomb squared.
Field is a vector describing force per unit charge; potential is a scalar describing energy per unit charge. Around a point charge the field falls as one over distance squared while the potential falls as one over distance, so they are never interchangeable.
Use superposition. Compute the field from each charge separately, then add the results as vectors, resolving into components if the charges are not in a straight line. Electrostatics is linear, so this addition is exact rather than approximate.
Because a dielectric medium polarises in response to the field, and the induced charges partly cancel the original field. Water has a relative permittivity near eighty, so the same charge produces a field about eighty times weaker in water than in air.
It is uniform well away from the edges. Near the plate boundaries the field lines bulge outward in what is called the fringing field, and the simple voltage-divided-by-separation formula no longer describes it accurately there.
Coulomb's law gives the force between two specified charges. This page gives the field a single charge creates at a point in space, whether or not another charge is present there. Multiply that field by a second charge and you recover Coulomb's law exactly.
This tool is provided for educational and study use. It models idealised point charges and infinite parallel plates, and does not account for conductor geometry, induced charges, shielding or dielectric breakdown, so treat its output as a physics result rather than an electrical safety assessment.
