The current ratio is a financial ratio that investors and analysts use to examine the liquidity of a company and its ability to pay shortterm liabilities (debt and payables) with its shortterm assets (cash, inventory, receivables). The current ratio is calculated by dividing current assets by current liabilities.
The quick ratio, on the other hand, is a liquidity indicator that filters the current ratio by measuring the amount of the most liquid current assets there are to cover current liabilities (you can think of the “quick” part as meaning assets that can be liquidated fast). The quick ratio, also called the “acidtest ratio,” is calculated by adding cash & equivalents, marketable investments and accounts receivables, and dividing that sum by current liabilities.
The main difference between the current ratio and the quick ratio is that the latter offers a more conservative view of the company’s ability to meets its shortterm liabilities with its shortterm assets because it does not include inventory and other current assets that are more difficult to liquidate (i.e., turn into cash). By excluding inventory (and other less liquid assets) the quick ratio focuses on the company’s more liquid assets.

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What is the formula for calculating the current ratio?
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Quick Ratio
The quick ratio is an indicator of a company’s shortterm liquidity. ... 
Current Ratio
The current ratio is a liquidity ratio measuring a company's ... 
Cash Asset Ratio
The current value of marketable securities and cash, divided ... 
Quick Liquidity Ratio
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