Electron Density Map Parameter Calculator
Size an electron density map before you calculate it: grid spacing, FFT dimensions, reflection counts and file size.
🗺️ What are Electron Density Map Parameters?
An electron density map is the three-dimensional picture of scattering density that comes out of a crystallographic Fourier transform. Before you can compute one, several practical numbers have to be fixed: how finely to sample the density onto a grid, what grid dimensions the FFT will actually accept, how many independent reflections the data contain, and how much disk space the resulting map will occupy. Those quantities all follow from three inputs, the unit cell dimensions, the resolution limit of the data, and the crystal's Laue symmetry.
Getting them right matters in day-to-day work. A grid that is too coarse produces a lumpy map where peak heights shift depending on where grid points happen to land, which makes automatic peak picking and real-space refinement unreliable. A grid dimension that is not built from small prime factors will be rejected outright by an FFT routine, or silently padded to a bigger size that wastes memory. And the unique reflection count is what you check a dataset's completeness against, and what sets the data-to-parameter ratio that decides whether you can refine anisotropic displacement parameters at all.
A common misconception is that a finer map grid improves resolution. It does not. Resolution is fixed by how far out in reciprocal space you actually measured intensities. Sampling more finely only interpolates the same band-limited function more smoothly. The sampling theorem says a spacing of d/2 already retains every bit of information in the map, and the reason crystallographers use d/3 instead is purely practical, it makes contoured features and peak heights insensitive to grid placement. A second misconception is that the theoretical reflection count is what you should measure. Real datasets always fall short of it, typically by 5 to 20 percent, because of the beamstop shadow, overloads, and the geometric blind region.
This calculator ties all of that together. Enter your cell, resolution and symmetry, and it returns the recommended grid spacing, the FFT-friendly grid dimensions rounded up to the next 2, 3, 5, 7-smooth even number on each axis, the total number of grid points, the map file size for a standard 4-byte-per-point CCP4 or MRC map, and both the total and symmetry-unique reflection counts. Two charts show how the reflection count explodes as you push to higher resolution, and how the map file size responds to your choice of sampling factor.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Tetragonal Protein Crystal at 2.0 Å
a = b = 79.1 Å, c = 37.9 Å, dmin = 2.0 Å, sampling factor 3, Laue 4/mmm
Example 2 — The Same Crystal Pushed to 1.5 Å
a = b = 79.1 Å, c = 37.9 Å, dmin = 1.5 Å, sampling factor 3, Laue 4/mmm
Example 3 — Small-Molecule Cubic Cell at 0.8 Å
a = b = c = 10 Å, dmin = 0.8 Å, sampling factor 3, Laue m-3m
Example 4 — Large Cubic Cell at Low Resolution
a = b = c = 200 Å, dmin = 3.5 Å, sampling factor 3, Laue m-3m
❓ Frequently Asked Questions
🔗 Related Calculators
What grid spacing should an electron density map use?
Use the resolution limit divided by 3 as the default. At 2.0 angstrom resolution that means a grid spacing of about 0.67 angstroms. Dividing by 2 is the Nyquist minimum and loses map detail, while dividing by 4 or more is used for density modification and averaging where smooth interpolation matters.
Why must FFT grid dimensions have small prime factors?
The fast Fourier transform is only fast when the transform length factorizes into small primes. Crystallographic FFT code typically supports factors of 2, 3, 5 and 7 only, so a dimension such as 179 (a prime) is rejected or padded. This calculator rounds each axis up to the next even number built from those factors.
How many unique reflections does a crystal give at a given resolution?
The count is approximately (4/3) pi V divided by d cubed, then divided by the order of the Laue group. For a 79.1 by 79.1 by 37.9 angstrom tetragonal cell at 2.0 angstroms with Laue class 4/mmm, that gives about 124,163 total lattice points and 7,760 unique reflections.
What is the Laue class multiplier for?
Symmetry makes many reflections equivalent, so only a fraction of reciprocal space is independent. The order of the Laue group, which already includes the inversion from Friedel's law, tells you that fraction: 2 for triclinic, 8 for orthorhombic, 16 for tetragonal 4/mmm, and 48 for cubic m-3m.
How big will my electron density map file be?
Multiply the three grid dimensions together and multiply by 4 bytes per point, which is the standard 32-bit float used in CCP4 and MRC map files. A 120 by 120 by 60 grid holds 864,000 points and occupies about 3.3 megabytes plus a small header.
Does a finer map grid improve resolution?
No. Resolution is set entirely by how far out in reciprocal space you measured data. A finer grid only samples the same density function more densely, which makes contours smoother and interpolation more accurate. Beyond about d/4 the extra points carry no new information at all.
What is Nyquist sampling in this context?
The map is a Fourier series band-limited at 1/d, so by the sampling theorem a spacing of d/2 is the coarsest that preserves all the information. In practice d/3 is used instead, because Nyquist sampling makes peak heights and contour shapes sensitive to exactly where the grid points happen to fall.
Why is the real reflection count lower than the calculated one?
The formula counts every reciprocal lattice point in a perfect sphere. Real datasets exclude very low angle reflections behind the beamstop, lose overloaded strong spots, miss the blind region set by the rotation geometry, and reject outliers, so a complete dataset typically records 80 to 95 percent of the theoretical count.
Does this calculator work for non-orthogonal unit cells?
It assumes all three cell angles are 90 degrees, so the volume is a times b times c. Monoclinic and triclinic cells have a smaller true volume than that product, and every result that depends on volume, meaning the reflection counts, scales down in proportion. Grid spacing and grid dimensions remain correct.
How does resolution change map and data size?
Both scale with the inverse cube of the resolution limit. Halving d from 3.0 to 1.5 angstroms multiplies the unique reflection count by eight and multiplies the number of grid points by eight as well, since the required grid spacing also halves along every axis.
What resolution counts as high resolution?
For macromolecules, better than 1.5 angstroms is high resolution and resolves individual atoms, 1.5 to 2.5 angstroms is the routine working range where side chains are clear, and worse than 3.0 angstroms shows only backbone and secondary structure. Small-molecule crystallography routinely reaches 0.8 angstroms.
Why is 4 bytes per grid point assumed?
CCP4 and MRC format maps store density as 32-bit floating point numbers by default, which is 4 bytes each. Some programs offer a 1-byte or 2-byte integer mode that shrinks the file four-fold or two-fold, at the cost of precision in the stored density values.