How to determine my portfolio's level of risk?

There are basically 2 types of risk - systematic and unsystematic risk. Systematic risk is known as the market risk, or the risk that all companies within the market are exposed to - for example in Singapore's STI, though DBS and Mapletree REIT is in different sectors of the market, market risks such as Singapore's economy growth rate and relations with our southeast Neighbours are all risks that affect all firms within Singapore due to it being a country's political risk. These risks cannot be diversified away, and are somewhat your "base risk" - meaning that no matter how diversified your portfolio is with no matter how many stocks in different sectors, you will still never be able to remove this risk exposure.

Unsystematic risk, or diversifiable risk, is firm or industry specific, and affect just that individual firm/industry. For example, the latest Elon Musk tweet scandal affects Tesla's stock, hence Elon Musk's unfiltered tweets are Tesla's "firm-specific risk", but it doesn't affect the agribusiness firms in America, for example.

These risks add to to form your portfolio's total risk - determined by standard deviation. Your systematic risk on the other hand, is determined by Beta, or the sensitivity of the firm's performance to the market's performance. Portfolio's beta can be determined by taking the weighted average of all the betas of the stocks within your portfolio, and the standard devation is determined through formulaic calculation regarding standard deviation of each individual stock within your porfolio and their correlations with one another. I will not explain further as I believe there is alot of materials available like Investopedia that explain this concept much better than I can over here.

Just make sure to be able to tolerate the level of risk you are able to take, and remember, there is no reward for taking unnecessary risks in the market!
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Unfortunately, risk is such a overloaded term that any answer you get will only be half useful.
You would have designed your portfolio for a certain objective? Anything that would make that objective difficult or unattainable would be risk.
Here are some general risks:
1. Concentration risk. Too much invested in a single Sector/geo/style/asset class
2.Volatility - huge volatility means greater chance of deviating from required return when you need it
3. Correlation - portfolio assets have high positive correlation with each other - evrrything goes up.or down together
4.quality risk - assets are not of good credit ratings
5.political risk - assets are subject to high political risk
6.liquidity risk - cant find buyers or sellers when you need to
7.some more miscellanous ones...but you get thr picture
You measure each of these differently. Which ones are relevant to you?