The Charge on the Electron Was Calculated by: Interactive Millikan Experiment Calculator
Use this premium calculator to estimate the charge on a suspended oil drop using the force balance from the classic oil drop experiment. The historical answer is Robert A. Millikan, whose measurements established the elementary charge with remarkable precision.
Electron Charge Calculator
Enter your oil drop experiment values below. This model uses the static balance equation for a suspended drop:
q = [(4/3)pi r^3 (rho_oil – rho_air) g] / E, where E = V / d
Chart and Interpretation
- This calculator assumes the oil drop is suspended, so electric force balances effective weight.
- The result is the total charge on the drop, not automatically a single electron.
- Dividing the drop charge by the elementary charge estimates how many excess electrons are on the drop.
- Real Millikan analysis also accounted for drag, terminal velocities, and small corrections.
Historical note: the accepted elementary charge today is exactly 1.602176634 x 10-19 coulomb by SI definition.
The charge on the electron was calculated by Robert A. Millikan
If you are asking, “the charge on the electron was calculated by whom?”, the standard historical answer is Robert Andrews Millikan. He is most famous for the oil drop experiment, a landmark physics investigation that measured the elementary electric charge with extraordinary accuracy for its time. Although J. J. Thomson had already shown that the electron existed and measured its charge-to-mass ratio, Millikan’s work provided the missing independent measurement of the electron’s actual charge. Once physicists knew the charge and the charge-to-mass ratio, they could also determine the electron’s mass.
This mattered enormously. Modern atomic theory, electronics, chemistry, and quantum physics all depend on the idea that electric charge is quantized. In practical language, that means charge comes in fundamental units. Millikan’s data strongly supported the conclusion that isolated charges on his oil drops were always whole-number multiples of a smallest unit, now called the elementary charge, denoted by e. Today the accepted value is exactly 1.602176634 x 10-19 coulomb.
What Millikan actually did
Millikan’s apparatus sprayed extremely small oil droplets into a chamber between two charged metal plates. Some droplets picked up electric charge through friction or ionization. By adjusting the voltage across the plates, he created an electric field that exerted an upward or downward force on a chosen droplet. When the electrical force balanced the effective weight of the droplet, the droplet could be made to hover almost motionless.
That balance condition gave the key idea:
- Gravitational force pulled the drop downward.
- Buoyant force from the surrounding air slightly reduced the effective weight.
- Electric force acted upward or downward depending on the sign of the charge and field direction.
When those forces balanced, the charge could be inferred from the electric field strength and the drop’s size. A simplified suspended-drop equation is the one used in the calculator above:
- Compute the electric field using E = V / d.
- Compute the effective weight using the drop volume and density difference (rho_oil – rho_air).
- Solve for charge from qE = (4/3)pi r^3 (rho_oil – rho_air)g.
In the original experiment, the procedure was more sophisticated than this simplified educational model. Millikan measured how droplets moved with and without the electric field, used viscous drag relationships, and introduced corrections to improve precision. Still, the core physical insight remains the same: balance known forces and infer the charge.
Why Millikan is often paired with J. J. Thomson
The phrase “the charge on the electron was calculated by” almost always leads to Millikan, but it helps to place his work in context. J. J. Thomson discovered the electron in cathode ray experiments and measured e/m, the charge-to-mass ratio. That was a major breakthrough, but it did not yet tell physicists the value of e itself. Millikan supplied that missing number. Once both values were known, scientists could compute the electron’s mass:
m = e / (e/m)
So a complete historical answer can be stated this way: J. J. Thomson discovered the electron and measured its charge-to-mass ratio, while Robert A. Millikan measured the elementary charge directly.
| Scientist | Key contribution | Approximate year | Why it mattered |
|---|---|---|---|
| J. J. Thomson | Measured electron charge-to-mass ratio, e/m | 1897 | Showed cathode rays were particles smaller than atoms |
| Robert A. Millikan | Measured the elementary charge, e, with oil drops | 1909 to 1913 | Established charge quantization and enabled electron mass calculation |
| Modern SI system | Defines e exactly as 1.602176634 x 10-19 C | 2019 onward | Provides a fixed exact value for standards and metrology |
How the oil drop experiment supports charge quantization
One of the most elegant outcomes of Millikan’s work was that measured drop charges were not random values. Instead, they clustered near integer multiples of a basic unit. For example, a droplet might carry charge close to 2e, 3e, 4e, and so on. That pattern was powerful evidence that electric charge is quantized. It also helped settle debates over whether charge was continuous or came in indivisible units.
This quantization remains central across physics:
- It explains ionic bonding and chemical valence behavior.
- It underlies current flow in electronic devices.
- It appears in particle physics, atomic transitions, and condensed matter systems.
- It supports precise electrical standards used in laboratories worldwide.
Accepted numerical value of the electron charge
Today the magnitude of the electron charge is exactly 1.602176634 x 10-19 C. Because the electron itself is negatively charged, its actual charge is written as:
electron charge = -1.602176634 x 10-19 C
Notice the distinction between the elementary charge and the charge of the electron. The symbol e usually refers to the positive magnitude. The electron has charge -e, while a proton has charge +e.
| Quantity | Symbol | Value | Meaning |
|---|---|---|---|
| Elementary charge magnitude | e | 1.602176634 x 10-19 C | Fundamental positive unit of charge |
| Electron charge | -e | -1.602176634 x 10-19 C | Charge carried by one electron |
| Proton charge | +e | +1.602176634 x 10-19 C | Equal magnitude, opposite sign to electron |
| Electron mass | me | 9.1093837015 x 10-31 kg | Found by combining e with Thomson’s e/m and later precision work |
What the calculator above teaches
The calculator on this page gives a simplified way to see the logic behind Millikan’s result. You enter the drop radius, plate voltage, plate spacing, and densities. The tool estimates the charge needed for the electric field to suspend the drop. Then it compares your answer with the accepted elementary charge and estimates how many electron charges your droplet likely contains.
If your result is, for example, several times larger than 1.602176634 x 10-19 C, that does not mean the calculation is wrong. It simply suggests the droplet may be carrying several excess electrons. In real data, the ratio q/e should be close to a whole number if the measurements are ideal.
Worked conceptual example
Suppose a very tiny oil drop has a radius around 1 micrometer, sits between plates separated by 5 millimeters, and is suspended by a 500 volt potential difference. For realistic oil and air densities, the resulting charge comes out on the same order of magnitude as a small multiple of the elementary charge. That is exactly the kind of pattern Millikan looked for repeatedly across many droplets.
The true genius of the experiment was not just a single calculation. It was the repeated observation that many independent measurements lined up with the same fundamental unit. That consistency transformed an isolated estimate into persuasive evidence for a universal constant.
Common misconceptions
- Misconception 1: Millikan discovered the electron. He did not. Thomson is credited with discovering the electron.
- Misconception 2: Millikan measured one electron on one drop. In reality, drops often carried multiple elementary charges.
- Misconception 3: The sign of charge is always shown in the quoted value. Often textbooks use e for magnitude only, while the electron is -e.
- Misconception 4: The experiment was simple. Historically, it required careful measurement, control of air behavior, and detailed corrections.
Why this topic still matters in modern science
Knowing the electron’s charge is not just a historical curiosity. It remains foundational in engineering and science. Every electric current is a rate of charge flow. Every capacitor stores charge. Every electrochemical reaction involves electron transfer. Semiconductor physics, battery design, microscopy, spectroscopy, and quantum devices all ultimately depend on the same elementary charge that Millikan measured.
In modern metrology, the elementary charge is especially important because the SI system now fixes its value exactly. This allows more stable and precise unit definitions. It also means the story of the electron charge connects classroom history directly to the way national and international measurement standards are built today.
Authoritative references
For further reading from trusted institutional sources, consult the following:
- National Institute of Standards and Technology (NIST): ampere and electrical units
- American Physical Society: SI redefinition and the elementary charge
- Encyclopaedia Britannica: Robert Millikan biography
Final answer
If you need the shortest direct response, here it is: the charge on the electron was calculated by Robert A. Millikan through the oil drop experiment. A fuller historical answer adds that J. J. Thomson discovered the electron and measured its charge-to-mass ratio, while Millikan measured the elementary charge itself. Together, those achievements became one of the pillars of modern physics.