The Cosmologist Calculator
(by Riccardo Scarpa)
Instructions

This calculator computes common quantities used in cosmology, like "luminosity distance" or "look back time", for any value of the Hubble constant H0 and the deceleration parameter q0. Function, however, are correct only for Friedmann-Robertson-Walker cosmologies in a matter dominated universe, whit the further restriction to models with cosmological constant equal to 0. This should cover the most common needs of astronomers.
Using the calculator, please keep in mind that some calculations require two input quantities (the redshift and another value), whereas others use only the redshift. To avoid ambiguity, the redshift is always entered in its own box: "Redshift goes here".
All other values are entered in the "Input Value" box. Results will always appear in the "Output Result" box (even when the result is a redshift). In some cases this may seems illogic, especially when inverting some function. However, we chose this approach to ensure all relevant values are visible at once.
The units associated to the input and output values are set automatically according to either the c.g.s. system, or to the most common astronomical units for that quantity (i.e., Mpc for distance). This means you never insert units. Rather, units are assumed to be as specified in the description of each function. Adopted units, for both input and output values, appear in the two boxes just below the Input and Output fields. When only the redshift is involved in the calculation, the "Input value" is automatically set to 0 and units erased to avoid ambiguity.



Description of each function

"z to age": returns the age of the universe in billions of years from redshift. The redshift must be entered in its box "Redshift goes here"; any value in the "Input value" field is unrelevant and automatically erased. The inverse of this function returns the redshift corresponding to a given age (in billions years) of the universe. The Age must be entered in the "Input Value" field.

"z to Distance": returns the proper distance in Mpc of an object at the specified redshift (entered in its box, not in the "Input value" field). If  the "Invert" is checked, then the redshift corresponding to a given distance in Mpc (to be entered in the "Input value" field) is returned. Note that the redshift will appear in the "Output result" box and not in the "Redshift goes here" box.

"z to Lum. dist.": as for the "z to distance" function but returns luminosity distance, which is (1+z) times the proper distance.

"Arcsec to kpc": converts angular dimension (in arcsecs) into kpc for an object at the given redshift. If "Invert Function" is checked, converts kpc into arcsecs.

"m to M": returns the absolute magnitude from apparent magnitude and redshift. If "Invert Function" is checked, converts absolute into apparent magnitudes.

"F to L bolom": convert flux in erg/s/cm^2 into luminosity in erg/s, for an object at the specified redshift. As units implies, both flux and luminosity are bolometric quantities. This is useful to compare flux and luminosity of, for istance, a single emission line, because the total flux from an emission line is a bolometric quantity. To convert a monocromatic flux, use the function "F to L". The inverse function convert a bolometric luminosity into flux.

"F to L": this button performs the same calculation of the button "F to L bolom", but in this case monocromatic fluxes and luminosities are considered. Flux must be in erg/s/cm^2/Angstrom, and luminosity in erg/s/Angstrom. The inverse function convert a monocromatic luminosity into flux.

"Look back Time": computes the look back time in Billions of years corresponding to the specified redshift. The inverse function is momentarily available for q0=0, sorry.

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