diff --git a/draftlogs/7901_fix.md b/draftlogs/7901_fix.md
new file mode 100644
index 00000000000..bf8a1a098bd
--- /dev/null
+++ b/draftlogs/7901_fix.md
@@ -0,0 +1 @@
+- Snap cartesian axis tick values to multiple of delta so custom `tickformat` (e.g. `"~r"`) no longer shows floating-point artifacts [[#7901](https://github.com/plotly/plotly.js/pull/7901)], with thanks to @arieleli01212 and @kirthi-b for the contribution!
diff --git a/src/plots/cartesian/axes.js b/src/plots/cartesian/axes.js
index 08bfda6f367..1929750d69e 100644
--- a/src/plots/cartesian/axes.js
+++ b/src/plots/cartesian/axes.js
@@ -90,6 +90,28 @@ function expandRange(range) {
     ];
 }
 
+/**
+ * Correct a floating-point roundoff artifact in a linearized tick value.
+ * When `l` is much closer to its nearest ideal grid position than one `dtick`
+ * (within `dtick * snapThreshold`), snap it to that ideal. Otherwise return
+ * `l` unchanged. See https://github.com/plotly/plotly.js/issues/7765.
+ *
+ * @param l - linearized tick value from the accumulator in calcTicks
+ * @param tick0l - the axis' `tick0` in linearized form
+ * @param dtick - the axis' tick step; must be numeric and nonzero to snap
+ * @returns the snapped value, or `l` unchanged if no snap applies
+ */
+function snapToGrid(l, tick0l, dtick) {
+    if (![dtick, l, tick0l].every(isNumeric) || dtick === 0) return l;
+
+    const nTicks = Math.round((l - tick0l) / dtick);
+    const idealTick = tick0l + nTicks * dtick;
+    const snapThreshold = 1e-6;
+    const shouldSnap = l !== idealTick && Math.abs(l - idealTick) < Math.abs(dtick) * snapThreshold;
+
+    return shouldSnap ? idealTick : l;
+}
+
 /*
  * find the list of possible axes to reference with an xref or yref attribute
  * and coerce it to that list
@@ -1067,6 +1089,7 @@ axes.calcTicks = function calcTicks(ax, opts) {
         }
 
         var dtick = mockAx.dtick;
+        var tick0l = (type === 'linear') ? mockAx.r2l(mockAx.tick0) : undefined;
 
         if(mockAx.rangebreaks && mockAx._tick0Init !== mockAx.tick0) {
             // adjust tick0
@@ -1110,7 +1133,7 @@ axes.calcTicks = function calcTicks(ax, opts) {
             if(tickVals.length > maxTicks || x === prevX) break;
             prevX = x;
 
-            var obj = { value: x };
+            var obj = { value: snapToGrid(x, tick0l, dtick) };
 
             if(major) {
                 if(isDLog && (x !== (x | 0))) {
diff --git a/test/jasmine/tests/axes_test.js b/test/jasmine/tests/axes_test.js
index 3d1e962312f..f1dac23af92 100644
--- a/test/jasmine/tests/axes_test.js
+++ b/test/jasmine/tests/axes_test.js
@@ -14,10 +14,7 @@ var Cartesian = require('../../../src/plots/cartesian');
 var Axes = require('../../../src/plots/cartesian/axes');
 var Fx = require('../../../src/components/fx');
 var supplyLayoutDefaults = require('../../../src/plots/cartesian/layout_defaults');
-var numerical = require('../../../src/constants/numerical');
-var BADNUM = numerical.BADNUM;
-var ONEDAY = numerical.ONEDAY;
-var ONEWEEK = numerical.ONEWEEK;
+const {BADNUM, MINUS_SIGN, ONEDAY, ONEWEEK} = require('../../../src/constants/numerical');
 
 var createGraphDiv = require('../assets/create_graph_div');
 var destroyGraphDiv = require('../assets/destroy_graph_div');
@@ -3502,6 +3499,50 @@ describe('Test axes', function() {
             ]);
         });
 
+        it('snaps a near-zero tick to exactly tick0', () => {
+            const spec = {
+                type: 'linear',
+                tickmode: 'linear',
+                tick0: 0,
+                dtick: 0.2,
+                range: [-0.65, 0.65]
+            };
+
+            expect(mockCalc({ ...spec, tickformat: '~r' })).toEqual([
+                MINUS_SIGN + '0.6',
+                MINUS_SIGN + '0.4',
+                MINUS_SIGN + '0.2',
+                '0',
+                '0.2',
+                '0.4',
+                '0.6'
+            ]);
+
+            // the default numeric format was already fine; make sure it stays fine
+            expect(mockCalc(spec)).toEqual([
+                MINUS_SIGN + '0.6',
+                MINUS_SIGN + '0.4',
+                MINUS_SIGN + '0.2',
+                '0',
+                '0.2',
+                '0.4',
+                '0.6'
+            ]);
+        });
+
+        it('snaps ticks to non-tick0 grid positions', () => {
+            const textOut = mockCalc({
+                type: 'linear',
+                tickmode: 'linear',
+                tick0: 1,
+                dtick: 0.1,
+                range: [-0.05, 0.05],
+                tickformat: '~r'
+            });
+
+            expect(textOut).toEqual(['0']);
+        });
+
         it('reverts to "power" for SI/B exponentformat beyond the prefix range (log case)', function() {
             var textOut = mockCalc({
                 type: 'log',