diff --git a/pysuperconductor/os_gap_calc.py b/pysuperconductor/os_gap_calc.py
index 59b362c..fc824ff 100644
--- a/pysuperconductor/os_gap_calc.py
+++ b/pysuperconductor/os_gap_calc.py
@@ -35,8 +35,19 @@ def find_gap(temp, mu_star, debye_frequency, nv):
 	return sol.x
 
 
+# this is n * Delta_0, calling it n in this file for brevity
 def n_integrand_function(xi, temp, delta, mu_star):
 	big_e = energy(xi, delta)
 	left = 1 / (1 + numpy.exp((big_e - mu_star) / temp))
 	right = 1 / (1 + numpy.exp(big_e / temp))
 	return left - right
+
+
+# as above, this is brevity n * Delta_0
+def n_integral(temp, delta, mu_star):
+	def integrand(xi):
+		return n_integrand_function(xi, temp, delta, mu_star)
+	intermediate = 20 * numpy.sqrt(delta ** 2 + mu_star ** 2)
+	lower = integrate.quad(integrand, 0, intermediate)[0]
+	upper = integrate.quad(integrand, intermediate, numpy.inf)[0]
+	return lower + upper
diff --git a/tests/test_os_gap_calc.py b/tests/test_os_gap_calc.py
index 61d5d24..2e6935f 100644
--- a/tests/test_os_gap_calc.py
+++ b/tests/test_os_gap_calc.py
@@ -55,3 +55,15 @@ def test_n_integrand_function():
 		decimal=7, err_msg='did not find correct n integrand value',
 		verbose=True
 	)
+
+
+def test_n_integral():
+	actual = None
+	with pytest.warns(None) as record:
+		actual = pysuperconductor.os_gap_calc.n_integral(2, 2, 1)
+	numpy.testing.assert_almost_equal(
+		actual, 0.478130649727604,
+		decimal=7, err_msg='did not find correct n integral value',
+		verbose=True
+	)
+	assert not record