The vegan package for R is pretty easy to use and can calculate a number of different indices by default.  You may also direct the software to calculate indices of your own construction.  If you are interested in species turnover, rarefaction, accumulation, or simply wish to decompose the diversity within your dataset into additive or multiplicative, vegan is a powerful tool.

However, just crunching a buncha numbers doesn't necessarily elucidate your questions, nor do they confidently test all of your hypotheses.  "Diversity" can refer to a number of independent (or interrelated) measures of community structure.  I would highly recommend works by Lou Jost (and others) that disentangle some of these interrelated measures and provide conceptual clarification for the use of particular metrics.

Just Google 'online diversity index calculator' and you will see 4 or 5 :-)

Please have a look at these links.

https://www.alyoung.com/labs/biodiversity_calculator.html

http://bpmsg.com/diversity-online-calculator/

I think EstimateS software will fit your study purpose. http://viceroy.colorado.edu/estimates/

All the best,

Shuhei

EstimateS can do most of the things you want to do. 

Good luck.

Biodiverse can be other software for your analysis, with advantages for geographic visualitacion of indexs.

http://biodiverse-analysis-software.blogspot.mx/

The vegan package for R is pretty easy to use and can calculate a number of different indices by default.  You may also direct the software to calculate indices of your own construction.  If you are interested in species turnover, rarefaction, accumulation, or simply wish to decompose the diversity within your dataset into additive or multiplicative, vegan is a powerful tool.

However, just crunching a buncha numbers doesn't necessarily elucidate your questions, nor do they confidently test all of your hypotheses.  "Diversity" can refer to a number of independent (or interrelated) measures of community structure.  I would highly recommend works by Lou Jost (and others) that disentangle some of these interrelated measures and provide conceptual clarification for the use of particular metrics.

Estimates is a good option. R package could work with Minitab or Arcgis if you decide make most deep science.

EstimateS, the vegan package in R or PaST. All three are good options for the standard diversity indexes.

The problem is that no one index or programme gives a full set of biodiversity quality indices as defined in my paper: Biodiversity Quality: a paradigm for biodiversity (Feest et al.). Check out my papers on Research Gate to see the possibilities of a plurality of indices that provide a rounded picture of biodiversity that allows change and difference to be measured. If you have difficulty in accessing the papers let me know and I will send themAlan Feest 

Estimate S software

http://chao.stat.nthu.edu.tw/wordpress/software_download/

Check this link

You can use SPADE - Species Prediction and Diversity Estimation to estimate biodiversity in communities and iNEXT (iNterpolation and EXTrapolation)

I think EstimateS software is very good option. Here is link

http://viceroy.eeb.uconn.edu/estimates/

I would suggest a visit to the site of Robert Colwell (http://viceroy.eeb.uconn.edu/Colwell/). And, if possible, I think it would be also a good option to consult the book of Anne Magurran, ‘Measuring biological diversity’.

http://www.flutterbys.com.au/stats/tut/tut13.2.html

The above link is useful to start with basic diversity indices calculation. You only need to know some basics of R programming.

PRIMER and PAST is good option for calculating Diversity Indices...

The PAST3.18 IS GOOD OPTION. BECAUSE MAKE BOOSTRAP 95% OF CONFIDENTIAL for all indices. Also realise diversity permutation test between comunity, determine too diversity alpha, beta.

You can use PCORD sofware.

Some package (“codyn”,"cytoDiv","flowDiv", "recluster","simboot","adiv","BiodiversityR","BioFTF","DiversityOccupancy","MBI","MCPAN","SpadeR") for R are pretty easy to use and can calculate a number of different indices by default.

> install.packages("packagefinder")

> library("packagefinder")

> search findPackage(search)

#12 out of 12978 CRAN packages found in 37 seconds.

Past 3.18

Hammer, Ø., D. A. T Harper y P. D. Ryan. 2018. PAST: Paleontological Statistics Software Package for Education and Data Analysis. Palaeontologia Electronica, 4: 1-9.

Estimate S is good for Accumulation curves … You can calculate Simpson's, Manson's and Rao2 ( the last two are functional trait indexes , so you need to have functional traits for the speacies) with http://botanika.bf.jcu.cz/suspa/FunctDiv.php.

This application might be useful if you only have your mobile on hand. It's on the early stage. However, it gives accurate Shannon diversity and evenness values. https://play.google.com/store/apps/details?id=com.paradise.diversity