Pricing Azure SQL database is difficult because various database service tier options such as database transaction units (DTU’s), max database size, disaster recovery options, and backup retention days are used to determine pricing instead of hardware (CPU/RAM/HD).  Generally I recommend starting out with a low service tier and scaling as your needs increase as it only takes a few minutes to scale with no downtime (see Change the service tier and performance level (pricing tier) of a SQL database).

DTU’s are explained at here.  To help, there is a Azure SQL Database DTU Calculator.  This calculator will help you determine the number of DTUs being used for your existing on-prem SQL Server database(s) as well as a recommendation of the minimum performance level and service tier that you need before you migrate to Azure SQL Database.  It does this by using performance monitor counters.

After you use a SQL Database for a while, you can use a pricing tier recommendation tool to determine the best service tier to switch to.  It does this by assessing historical resource usage for a SQL database.

Note this pricing is per database, so if you have many databases on each on-prem SQL server you will have to price each one.  But there are many “built-in” features of SQL database, such as high availability and disaster recovery, that you don’t have to build or manage in the cloud, thus saving you costs and administration time.

You pay for each database based on up-time.  You don’t pay for storage (but there is a database size limit for each tier).

Below is the pricing for all database service tiers, based in the East US region, for the single database model (pricing is different for elastic database pools which are an option to share resources).  The pricing comes from the Azure pricing calculator:

Basic, SQL Database, 5 DTU, 2GB DB, $5/month
Standard, S0, SQL Database, 10 DTU, 250GB database, $15/month
Standard, S1, SQL Database, 20 DTU, 250GB database, $30/month
Standard, S2, SQL Database, 50 DTU, 250GB database, $75/month
Standard, S3, SQL Database, 100 DTU, 250GB database, $150/month
Premium, P1, SQL Database, 125 DTU, 500GB database, $465/month
Premium, P2, SQL Database, 250 DTU, 500GB database, $930/month
Premium, P4, SQL Database, 500 DTU, 500GB database, $1,860/month
Premium, P6, SQL Database, 1000 DTU, 500GB database, $3,720/month
Premium, P11, SQL Database, 1750 DTU, 1TB database, $7,001/month
Premium, P15, SQL Database, 4000 DTU, 1TB database, $16,003/month

For more details on pricing, see SQL Database Pricing.  Data going into a SQL Database is free (“Inbound data transfers”).  Data going out of a SQL Database is free (“Outbound data transfers”) if within the same Azure data center (“region”), otherwise there is a small cost – see Data Transfers Pricing Details.

An option to get around the 1TB database size limit is to split the data into multiple databases and use elastic database queries.

More info:

Understanding Windows Azure Storage Billing – Bandwidth, Transactions, and Capacity

Understand your bill for Microsoft Azure

Azure SQL Database – How to choose the right service tier