de Broglie Wavelength Calculator

How it is calculated

Enter the particle's mass in kilograms and its speed in metres per second. The tool computes momentum p = m × v and then the de Broglie wavelength λ = h / |p|, with Planck's constant h = 6.62607015×10⁻³⁴ J·s. It reports the momentum in kg·m/s and the wavelength in metres, nanometres and picometres, all in scientific notation with four decimals, such as 7.2742e-10.

Mass must be above zero and velocity cannot be zero, since a particle at rest has no defined wavelength here. A negative velocity gives a negative momentum but the same wavelength, because the absolute value is used. The formula is the non-relativistic one: p = m × v becomes inaccurate as the speed approaches the speed of light (about 3×10⁸ m/s), and the tool does not warn about it. Enter small numbers in the form 9.109e-31.

Common mistakes

• Entering mass in grams or atomic mass units. The tool needs kilograms; an electron is 9.109e-31 kg, not 9.109e-28 g typed as is.
• Entering speed in km/s or as a fraction of the speed of light. It must be m/s, so 0.01c is about 3e6.
• Using the tool for particles near light speed. The simple p = m × v rule underestimates momentum there, so the wavelength it returns is too long.
• Expecting a measurable wavelength for everyday objects. A 0.145 kg ball at 40 m/s gives 1.1424e-34 m, far smaller than any atom, so wave behaviour never shows.
• Misreading the exponent. 7.2742e-1 nm means 0.72742 nm, and the e-notation is easily taken for a much larger or smaller number.