String Expression to be evaluated to number

I don't think that is possible in a user defined function.

You could do it in a stored procedure, like:

declare @calc varchar(max)
set @calc = '10*4.5*0.5'

declare @sql nvarchar(max)
declare @result float
set @sql = N'set @result = ' + @calc
exec sp_executesql @sql, N'@result float output', @result out
select @result

But dynamic SQL, like exec or sp_executesql, is not allowed in user defined functions.

Disclaimer: I'm the owner of the project Eval SQL.NET

For SQL 2012+, you can use Eval SQL.NET which can be run with SAFE Permission.

The performance is great (better than UDF) and honors operator precedence and parenthesis. In fact, almost all the C# language is supported.

You can also specify parameters to your formula.

-- SELECT 225.00
SELECT 10 * CAST(SQLNET::New('10*4.5*0.5').Eval() AS DECIMAL(18, 2))

-- SELECT 70
DECLARE @formula VARCHAR(50) = 'a+b*c'
SELECT  10 * SQLNET::New(@formula)
                    .Val('a', 1)
                    .Val('b', 2)
                    .Val('c', 3)
                    .EvalInt()