De Broglie Wavelength Calculator

Every moving particle has a wave nature, with wavelength λ = h/p, where h is Planck's constant (6.626×10³ J·s) and p is momentum in kg·m/s. For a particle of mass m and velocity v, p = mv, so λ = h/(mv). An electron moving at 10 m/s has λ ≈ 6.626×10³ / (9.11×10³¹ × 10) ≈ 7.3×10^8¹ m, around the size of an atom. This idea, proposed by Louis de Broglie in 1924, links classical particles to quantum waves and underpins electron microscopes.

Enter the mass in kilograms and velocity in m/s, and the tool returns wavelength using λ = h/(mv). Output usually appears in metres or nanometres. For an electron (m = 9.11×10³¹ kg) at 2×10^8 m/s, you'd get λ ≈ 3.6×10¹ m. The calculator is particularly handy when masses are tiny — those exponents stack up quickly and a missed minus sign throws the answer off by orders of magnitude. Always double-check that mass is in kilograms, not grams or atomic mass units.

When the momentum p is already known, you skip the mass-and-velocity step and go straight to λ = h/p. Planck's constant h = 6.626×10³ J·s, momentum is in kg·m/s, and wavelength comes out in metres. For p = 10² kg·m/s, λ = 6.626×10³ / 10² ≈ 6.6×10¹ m. This direct version is useful in particle physics when momentum is given through an accelerator's energy, or when you've already computed relativistic momentum and don't want to back-track to v.

Plug in the electron's mass m = 9.109×10³¹ kg and its velocity, and you'll get λ. A common physics problem involves an electron accelerated through a voltage V, where eV = ½mv² gives the speed, then λ = h/(mv) follows. For a 100 V acceleration, the electron reaches about 5.93×10^8 m/s, giving λ ≈ 1.23×10^8¹ m, close to atomic spacing. That's why electrons make excellent diffraction probes for crystal structures — their wavelength matches atom-to-atom distances perfectly.

Same idea as before: compute momentum first using p = mv, then divide Planck's constant by it: λ = h/(mv). The calculator does this in one shot once you supply mass (kg) and velocity (m/s). For a 0.05 kg ball thrown at 30 m/s, λ ≈ 6.626×10³ / 1.5 ≈ 4.4×10³ m — absurdly small, far below any measurable scale. That's exactly why we don't see baseballs diffract. The matter-wave is real, but for everyday objects it's so tiny it never shows up.

Because their wavelengths are mind-bogglingly small. A 1 kg cricket ball moving at 20 m/s has λ ≈ 3×10^8³ m, which is many trillion times smaller than an atomic nucleus. Diffraction or interference patterns require an opening or barrier comparable to the wavelength, and nothing physical comes anywhere close to those scales. Electrons and atoms have wavelengths in the nanometre or picometre range, so they readily show wave behaviour through crystals or slits. Mass kills the wavelength, which is why the quantum world stays quietly hidden in our daily life.

Stick with SI inputs to keep things tidy: mass in kilograms, velocity in metres per second, momentum in kg·m/s, and Planck's constant 6.626×10³ J·s. The output wavelength comes out in metres, but for typical particle physics it's far easier to read in nanometres (10^-6 m) or picometres (10¹² m). Calculators usually convert automatically. If you slip in grams or centimetres, every factor of 1000 amplifies through the equation. The neat thing about de Broglie's relation is that the units always work out cleanly if you're disciplined at the start.