In Apex you can use "describe" calls. If all other options fail - you could build a custom service that returns this data to you.
Schema.DescribeFieldResult dfr = Account.Address__c.getDescribe();
System.debug(dfr.getCalculatedFormula());
// BillingStreet & BR() & BillingCity & BR() &  BillingPostalCode & BR() &  BillingCountry & BR() &  Street2__c & BR() & Street3__c
You've tagged metadata API so if you really use that - similar info should be available in it.
<CustomField>
    <fullName>Address__c</fullName>
    <externalId>false</externalId>
    <formula>BillingStreet & BR() & BillingCity & BR() &  BillingPostalCode & BR() &  BillingCountry & BR() &  Street2__c & BR() & Street3__c</formula>
    <formulaTreatBlanksAs>BlankAsZero</formulaTreatBlanksAs>
    <label>Address</label>
    <required>false</required>
    <trackHistory>false</trackHistory>
    <type>Text</type>
    <unique>false</unique>
</CustomField>
In REST API it's similar, a call to /services/data/v48.0/sobjects/Account/describe will return (among others)
{
    "aggregatable" : true,
    "aiPredictionField" : false,
    "autoNumber" : false,
    "byteLength" : 3900,
    "calculated" : true,
    "calculatedFormula" : "BillingStreet & BR() & BillingCity & BR() &  BillingPostalCode & BR() &  BillingCountry & BR() &  Street2__c & BR() & Street3__c",
    "cascadeDelete" : false,
    (...)
    "formulaTreatNullNumberAsZero" : true,
    "groupable" : false,
    "highScaleNumber" : false,
    "htmlFormatted" : true,
    "idLookup" : false,
    "inlineHelpText" : null,
    "label" : "Address",
    "length" : 1300,
    "mask" : null,
    "maskType" : null,
    "name" : "Address__c",
    (...)
    "type" : "string",
    "unique" : false,
    "updateable" : false,
    "writeRequiresMasterRead" : false
  }
And finally there's Tooling API where you can query the metadata like you'd query normal database tables. But the core of what you need will be hidden in a JSON field you'd have to parse. If your tool is some ETL - check if it can query FieldDefinition table.
/services/data/v48.0/tooling/query?q=SELECT+Metadata+FROM+FieldDefinition+WHERE+EntityDefinitionId+=+'Account'+AND+QualifiedApiName+=+'Address__c'
Hope this helps!
Check out this  Online Salesforce Course to learn more.
Thanks!