How many characters can a Java String have?

While you can in theory Integer.MAX_VALUE characters, the JVM is limited in the size of the array it can use.

public static void main(String... args) {
    for (int i = 0; i < 4; i++) {
        int len = Integer.MAX_VALUE - i;
        try {
            char[] ch = new char[len];
            System.out.println("len: " + len + " OK");
        } catch (Error e) {
            System.out.println("len: " + len + " " + e);
        }
    }
}

on Oracle Java 8 update 92 prints

len: 2147483647 java.lang.OutOfMemoryError: Requested array size exceeds VM limit
len: 2147483646 java.lang.OutOfMemoryError: Requested array size exceeds VM limit
len: 2147483645 OK
len: 2147483644 OK

Note: in Java 9, Strings will use byte[] which will mean that multi-byte characters will use more than one byte and reduce the maximum further. If you have all four byte code-points e.g. emojis, you will only get around 500 million characters

Have you considered using BigDecimal instead of String to hold your numbers?

You should be able to get a String of length

1. Integer.MAX_VALUE always 2,147,483,647 (2³¹ - 1)
   (Defined by the Java specification, the maximum size of an array, which the String class uses for internal storage)
   OR

2. Half your maximum heap size (since each character is two bytes) whichever is smaller.

I believe they can be up to 2^31-1 characters, as they are held by an internal array, and arrays are indexed by integers in Java.