Coulomb's Law Calculator: F = k·q1·q2 / r²

Real-world use cases

• Check a physics homework answer in seconds

  You worked out the force between a 3 µC and a -2 µC charge 5 cm apart by hand and want to be sure. Type the charges, set the unit to µC, set the distance to 5 cm, and read F = -21.6 N — negative, so attractive, exactly as the opposite signs predict. The worked steps line up with your scratch paper so you can spot where a stray exponent or a dropped square crept in.

• Build and grade problem sets as a teacher

  Setting an electrostatics quiz, you need clean numbers that solve to tidy answers. Try charge pairs and separations until the force lands on a round value, then flip to the reverse modes to confirm the distance and charge solutions match. Paste the share link into the answer key so every student lands on the same fully worked example.

• Compare the electric and gravitational force on the same pair

  For a proton and an electron 1 nm apart, this tool gives an electrostatic attraction of about -2.3e-10 N. Run the gravitational-force calculator on the same two particles and the gravitational pull is roughly 1e-67 N — about 39 orders of magnitude weaker. Putting both numbers side by side makes the relative strength of the two forces concrete rather than abstract.

• Size the charge for a demo or a lab estimate

  You want two pith balls to repel with a force you can actually see at 2 cm. Switch to Charge mode, enter the target force and the distance, set the other charge, and the tool returns the charge you need. It tells you in advance whether the experiment calls for nanocoulombs or microcoulombs, so you do not chase a result that the apparatus cannot reach.

Common pitfalls

• Forgetting the inverse square. The force depends on r², not r, so doubling the distance quarters the force rather than halving it. Plugging in r instead of r² is the single most common slip and it makes close-range forces look four-plus times too small.

• Mixing charge units. A µC is 1e-6 C and a nC is 1e-9 C, a factor of a thousand apart. Typing 5 while the unit selector still reads C treats five microcoulombs as five whole coulombs and inflates the force by a trillion. Always check the unit selector before reading the answer.

• Reading the sign as a magnitude. A force of -21.6 N is not weaker than +21.6 N. The minus sign only means attraction, not a smaller force. Compare magnitudes by absolute value and use the sign solely to tell repulsion from attraction.

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