Hobby calculators · astronomy and microscopy
The sums hobbyists keep redoing.
A Bortle class is not a limiting magnitude, a scale bar depends on the adapter as well as the objective, and an exposure limit depends on whether the mount tracks. Each calculator here does one of those sums, shows the formula, and cites where it comes from.
SQM to Bortle and NELM Converter
Turn a Sky Quality Meter reading in mag/arcsec² into a naked-eye limiting magnitude and a Bortle class
Microscope Scale Bar Calculator
Work out micrometres per pixel and how many pixels a scale bar should be
NPF Rule Calculator
Calculate the longest night-sky exposure before stars trail with the NPF rule
Custom Horizon File Generator for N.I.N.A. and Telescopius
Paste azimuth and altitude readings from your backyard
Sub Exposure Calculator for Astrophotography
Work out how long each astrophotography sub-exposure should be from camera read noise and your sky background
Polar Alignment Star Trail Calculator
Find the longest unguided sub-exposure your polar alignment error allows
Miniature Scale Converter
Figure height in mm to a 1:x ratio for any person height, with the nearest common scale and a size table.
Airbrush Thinner Ratio Calculator
Paint to thinner, thinner to paint or percent into ml for your cup, plus thinner to add to paint you have.
Jigsaw Puzzle Table Size Calculator
The area needed to lay every piece flat, from the finished size, using the square-root-of-3 rule from a published paper.
Jigsaw Puzzle Time Calculator
Median solve times for 100 to 2000 pieces for one person, a pair or a team, with the middle-50% range and sessions needed.
Puzzle Board Size Calculator
The board you need for the finished puzzle plus a margin, checked against Galison guidance and your own board.
Dollhouse LED Lighting Calculator
LEDs per series string, a resistor for each string, total current and 9 V battery run time. Battery power only.
Rear Derailleur Capacity Calculator
Chain-wrap capacity from your chainrings and cassette, checked against published total, front-difference and largest-cog limits.
Cycling Climb Time Saved per kg
Seconds saved on a climb by losing weight, from the standard power-balance equations.
Cycling Climb to Flat Distance Equivalent
How many flat kilometres at the same power take as long as a climb.
Fishing Line Reel Capacity Calculator
How much line fits when you change line diameter, or the diameter that gets a target length.
UK Degree Classification Calculator
Your class under three published university schemes or your own weighting.
Multicolor 3D Print Purge Waste Calculator
Grams wasted on flushes and the prime tower from your colour-change count, with waste per copy and the saving from a lower multiplier.
3D Printer Electricity Cost Calculator
kWh and cost per print, per hour and per month from average watts, with maker power figures and the US average rate.
G-code Print Time and Filament Estimator
Open a sliced file in your browser for filament length, weight, cost, move time, size and layers. Nothing is uploaded.
3D Print Rotated Fit Calculator
Will a long part fit the bed turned on the plate? The angle that works and the longest part of a given width.
Model Railroad Minimum Radius Calculator
Free model railroad minimum radius calculator: enter your locomotive wheelbase or length and your longest cars, and get the NMRA RP-11 class and the minimum curve radius in HO, N, O, S, OO or TT.
Model Railroad Helix Calculator
Free model railroad helix calculator: enter the radius and grade to get the circumference, the rise per turn, the turns and track length for a target height, and whether each turn clears the track below.
Model Railroad Riser and Grade Calculator
Free model railroad riser calculator: from a grade and a run, get the height at every riser, or from the height you need to clear, get the run required, with the NMRA clearance height for your scale and era.
Model Railroad Vertical Transition Calculator
Free vertical transition calculator for model railroads: enter the two grades and the length of the easement to get the rate of change and the height of the track at each point, or find the length for a rate you choose.
Model Railroad Scale Miles Converter
Free model railroad scale miles converter: turn a real distance into model feet and inches, or a length of model track into scale feet and miles, for HO, N, O, S, OO, TT and Z using NMRA scale ratios.
Model Railroad Yard and Siding Capacity Calculator
Free model railroad siding capacity calculator: enter the usable length of a siding or yard track, the car and locomotive lengths and your coupler gap, and get how many cars fit, in any scale.
DCC Booster and Power Calculator
Free DCC booster calculator: enter the locomotives running, idle locomotives and lit passenger cars to get the total amps, using Digitrax planning figures, and the number of 5 amp or 8 amp boosters.
Where these came from
Each tool answers a question people were asking in public threads: how to convert sky brightness into a Bortle class, how long a scale bar should be in pixels, how to clean up a horizon file for planning software, and how long a sub-exposure can run. The pages work from numbers you enter, run in your browser, and send nothing anywhere.
Where the numbers come from
The scale table comes from Wikipedia’s miniature wargaming article. The airbrush starting points come from Tamiya’s enamel product page and from posters in FineScale Modeler threads, and are reports rather than specifications. Related: the LEGO stud and scale converter and the paint mixing ratio calculator.
Where the numbers come from
The table size tool uses the square-root-of-3 result from a 2023 arXiv paper by Bonsma-Fisher and Bonsma-Fisher. Solve times are medians from MySpeedPuzzling. Finished sizes are copied from Buffalo Games, White Mountain and Galison pages and Galison's table-space chart. The LED planner uses Vishay 5 mm LED forward voltages, the Energizer 522 datasheet and a Core Electronics forum thread. All are fan-made and not affiliated with any maker. Related: the LED resistor calculator.
Where the numbers come from
The cycling tools use the power equations in Wikipedia's Bicycle performance article. The derailleur tool uses Sheldon Brown's capacity entry and published limits from Shimano's RD-7700 instructions and a Mantel listing. Fishing line capacity uses Omni Calculator's cylinder-volume formula. The degree calculator follows pages from Keele, UWE Bristol and Manchester Metropolitan University. All are independent and not affiliated with those sources.
Where the numbers come from
Purge figures come from Bambu Lab’s wiki page on reducing filament-change waste. Power figures are Prusa’s MK4S page and Bambu Lab’s A1 specification sheet, priced at the U.S. EIA’s August 2026 average. The G-code tool follows Marlin’s documentation and is checked against PrusaSlicer’s sample file. The fit tool is plane geometry, tested against a published criterion. Nothing here is affiliated with a printer maker. Related: the 3D print filament cost calculator.
Where the numbers come from
Curve radius classes, scale ratios and clearance heights are read from the NMRA's RP-11, S-3.2 and RP-7.1. DCC current figures are Digitrax's own planning numbers from its Tech Support Depot. The vertical transition tool uses the rate-of-change definition from a Caltrans sheet. Each page lists its sources with the date they were read. All are fan-made and not affiliated with any maker or standards body.