Is there any webpage which has a direct black scholes equation that solve for implied volatility or a detail tutorial?

You cannot solve for volatility in Black Scholes hence the reason that iteration is necessary. If you're not familiar with iteration, it's where you enter a sequence of successive numbers for one variable (volatility) which yields an answer successively closer to a desired answer (the premium). The input that yields the match is the answer, aka the implied volatility.

the calculator is great but want a direction bsm equation that solve for volatility. Give all the bsm variables AND call or put quote, solve for volatility. Tried googling for the equation but most give the standard C = S N(d1) - K e-rT N(d2) but that does not directly solve for volatility symbol at d1 and d2

As spindr0 points out, you'll need to go through various iterations to back out the IV values given your BSM equation. It cannot be solved analytically. This can be done manually using the calculator - take the call price and keep changing the IV until your calculator price matches that of the market. To do this automatically in excel you'll have to use the solver function to match your BSM equation price to that of the market.

why is that sdpr sector index has implied volatility. The webpage that list the implied volatility does not say which options strike the calculation is made from. Isn't the bsm require strike price for the model? optionxpress also has implied volatility which also don't depend on strike price but they said their model is bsm. They have the same implied volatility chart for all options strike some posters post implied volatility of different period 10 days 20 days calculated from bsm but the model don't have period for variables so how do they derive the different period implied volatility?

It's usually calculated as an index similar to VIX calculation. Some providers just calculate an ATM IV volatility.

have you ever heard of the word AVERAGE? You Keep asking the same question over and over. Do u bother to read the replies?