Bragg law interplanar spacing calculator

It applies the standard relation n lambda equals 2 d sine theta and reports the resulting spacing in metres, nanometres, picometres, and ångströms. The calculation is deterministic and runs without external data, making it useful for checking diffraction measurements, teaching crystallography, and preparing repeatable laboratory workflows.

Enter the angle that Bragg law actually uses

The angle in the equation is the Bragg angle theta: the angle between the incident X-ray beam and the reflecting lattice plane. In many diffractometer outputs, the horizontal axis is labelled 2 theta because the instrument records the angle between the incident and diffracted beams. If your measured peak position is reported as 2 theta, divide that value by two before entering it as angle_deg. Confusing theta with 2 theta is one of the most common reasons for obtaining an incorrect interplanar spacing. The calculator accepts angles strictly between zero and ninety degrees. It evaluates the sine after converting degrees to radians internally, so the input remains familiar to laboratory users. Choose the peak position consistently, ideally after background subtraction and peak fitting when measurement precision matters. The result inherits uncertainty from the measured angle: at small angles, a modest angular error can noticeably alter the calculated spacing. This tool calculates the central value only and does not infer an uncertainty interval from instrument resolution or peak width.

Match the wavelength and diffraction order to the experiment

Enter the X-ray wavelength as a positive number and select its unit explicitly. Ångströms are common in crystallography, while nanometres, picometres, and metres are also supported. For example, Cu K-alpha radiation is often represented by a wavelength near 1.54 ångströms, but you should use the wavelength appropriate to the source, line selection, and calibration behind your measurement. The diffraction order n must be a positive integer. Most routine powder-diffraction indexing uses first-order reflections, so n equals one is usually the appropriate starting point. A higher order means that the path difference spans multiple wavelengths and therefore produces a proportionally larger calculated d value for the same wavelength and angle. Do not use the Miller indices as the diffraction order: an index such as (111) identifies a plane family, whereas n is the integer in Bragg's equation. The calculator keeps these concepts separate and limits the order to 100, which is ample for practical calculations while preventing accidental extreme input.

Interpret and verify the calculated plane spacing

The algorithm rearranges Bragg's law, n lambda equals 2 d sine theta, to obtain d equals n lambda divided by twice the sine of theta. It first converts the chosen wavelength unit to metres, performs the calculation, and then presents the same physical spacing in four units. Reporting multiple units makes the result easier to compare with crystallographic tables, simulation output, and software that may use different conventions. A numerical result alone does not identify the material or assign Miller indices. Compare the spacing with reference patterns only after considering phase composition, systematic absences, calibration, strain, and possible peak overlap. You can also check the calculation by substituting the returned d value into the original equation; both sides should agree to the displayed precision. The calculation assumes monochromatic radiation and the usual geometric form of Bragg's law. It does not correct for wavelength doublets, specimen displacement, refraction, instrumental zero shift, or uncertainty. For automated use, the API charges $0.002 per request; the browser calculation uses the same deterministic core logic.